Using Structure to Rewrite Expressions - Algebra 2
Card 1 of 30
What is $9x^2-25$ factored using structure?
What is $9x^2-25$ factored using structure?
Tap to reveal answer
$(3x-5)(3x+5)$. Recognizes $(3x)^2-5^2$ as difference of squares.
$(3x-5)(3x+5)$. Recognizes $(3x)^2-5^2$ as difference of squares.
← Didn't Know|Knew It →
Identify the rewrite that shows $x^4-y^4$ as a difference of squares.
Identify the rewrite that shows $x^4-y^4$ as a difference of squares.
Tap to reveal answer
$x^4-y^4=(x^2)^2-(y^2)^2$. Recognizes $x^4$ as $(x^2)^2$ and $y^4$ as $(y^2)^2$.
$x^4-y^4=(x^2)^2-(y^2)^2$. Recognizes $x^4$ as $(x^2)^2$ and $y^4$ as $(y^2)^2$.
← Didn't Know|Knew It →
What is $x^2-5x+6$ factored using structure?
What is $x^2-5x+6$ factored using structure?
Tap to reveal answer
$(x-2)(x-3)$. Find two numbers that multiply to $6$ and add to $-5$: $-2$ and $-3$.
$(x-2)(x-3)$. Find two numbers that multiply to $6$ and add to $-5$: $-2$ and $-3$.
← Didn't Know|Knew It →
Identify the rewrite that shows $x^4-y^4$ as a difference of squares.
Identify the rewrite that shows $x^4-y^4$ as a difference of squares.
Tap to reveal answer
$x^4-y^4=(x^2)^2-(y^2)^2$. Recognizes $x^4$ as $(x^2)^2$ and $y^4$ as $(y^2)^2$.
$x^4-y^4=(x^2)^2-(y^2)^2$. Recognizes $x^4$ as $(x^2)^2$ and $y^4$ as $(y^2)^2$.
← Didn't Know|Knew It →
What is $x^4-y^4$ factored completely over the integers?
What is $x^4-y^4$ factored completely over the integers?
Tap to reveal answer
$(x-y)(x+y)(x^2+y^2)$. Factor difference of squares twice: $(x^2-y^2)(x^2+y^2) = (x-y)(x+y)(x^2+y^2)$.
$(x-y)(x+y)(x^2+y^2)$. Factor difference of squares twice: $(x^2-y^2)(x^2+y^2) = (x-y)(x+y)(x^2+y^2)$.
← Didn't Know|Knew It →
What is $9x^2-25$ factored using structure?
What is $9x^2-25$ factored using structure?
Tap to reveal answer
$(3x-5)(3x+5)$. Recognizes $(3x)^2-5^2$ as difference of squares.
$(3x-5)(3x+5)$. Recognizes $(3x)^2-5^2$ as difference of squares.
← Didn't Know|Knew It →
What is $16a^2b^2-81$ factored using structure?
What is $16a^2b^2-81$ factored using structure?
Tap to reveal answer
$(4ab-9)(4ab+9)$. Recognizes $(4ab)^2-9^2$ as difference of squares.
$(4ab-9)(4ab+9)$. Recognizes $(4ab)^2-9^2$ as difference of squares.
← Didn't Know|Knew It →
What is $49m^2n^2-1$ factored using structure?
What is $49m^2n^2-1$ factored using structure?
Tap to reveal answer
$(7mn-1)(7mn+1)$. Recognizes $(7mn)^2-1^2$ as difference of squares.
$(7mn-1)(7mn+1)$. Recognizes $(7mn)^2-1^2$ as difference of squares.
← Didn't Know|Knew It →
What is $x^2+10x+25$ rewritten as a perfect square?
What is $x^2+10x+25$ rewritten as a perfect square?
Tap to reveal answer
$(x+5)^2$. Recognizes $x^2+2(x)(5)+5^2$ as perfect square trinomial.
$(x+5)^2$. Recognizes $x^2+2(x)(5)+5^2$ as perfect square trinomial.
← Didn't Know|Knew It →
What is $y^2-12y+36$ rewritten as a perfect square?
What is $y^2-12y+36$ rewritten as a perfect square?
Tap to reveal answer
$(y-6)^2$. Recognizes $y^2-2(y)(6)+6^2$ as perfect square trinomial.
$(y-6)^2$. Recognizes $y^2-2(y)(6)+6^2$ as perfect square trinomial.
← Didn't Know|Knew It →
What is $4x^2+12x+9$ rewritten as a perfect square?
What is $4x^2+12x+9$ rewritten as a perfect square?
Tap to reveal answer
$(2x+3)^2$. Recognizes $(2x)^2+2(2x)(3)+3^2$ as perfect square trinomial.
$(2x+3)^2$. Recognizes $(2x)^2+2(2x)(3)+3^2$ as perfect square trinomial.
← Didn't Know|Knew It →
What is $25p^2-30p+9$ rewritten as a perfect square?
What is $25p^2-30p+9$ rewritten as a perfect square?
Tap to reveal answer
$(5p-3)^2$. Recognizes $(5p)^2-2(5p)(3)+3^2$ as perfect square trinomial.
$(5p-3)^2$. Recognizes $(5p)^2-2(5p)(3)+3^2$ as perfect square trinomial.
← Didn't Know|Knew It →
What is $x^3+8$ factored using structure?
What is $x^3+8$ factored using structure?
Tap to reveal answer
$(x+2)(x^2-2x+4)$. Recognizes $x^3+2^3$ and applies sum of cubes formula.
$(x+2)(x^2-2x+4)$. Recognizes $x^3+2^3$ and applies sum of cubes formula.
← Didn't Know|Knew It →
What is $27a^3-b^3$ factored using structure?
What is $27a^3-b^3$ factored using structure?
Tap to reveal answer
$(3a-b)(9a^2+3ab+b^2)$. Recognizes $(3a)^3-b^3$ and applies difference of cubes formula.
$(3a-b)(9a^2+3ab+b^2)$. Recognizes $(3a)^3-b^3$ and applies difference of cubes formula.
← Didn't Know|Knew It →
What is $64t^3+125$ factored using structure?
What is $64t^3+125$ factored using structure?
Tap to reveal answer
$(4t+5)(16t^2-20t+25)$. Recognizes $(4t)^3+5^3$ and applies sum of cubes formula.
$(4t+5)(16t^2-20t+25)$. Recognizes $(4t)^3+5^3$ and applies sum of cubes formula.
← Didn't Know|Knew It →
What is $8x^3-1$ factored using structure?
What is $8x^3-1$ factored using structure?
Tap to reveal answer
$(2x-1)(4x^2+2x+1)$. Recognizes $(2x)^3-1^3$ and applies difference of cubes formula.
$(2x-1)(4x^2+2x+1)$. Recognizes $(2x)^3-1^3$ and applies difference of cubes formula.
← Didn't Know|Knew It →
What is $x^2-81$ factored using structure?
What is $x^2-81$ factored using structure?
Tap to reveal answer
$(x-9)(x+9)$. Recognizes $x^2-9^2$ as difference of squares.
$(x-9)(x+9)$. Recognizes $x^2-9^2$ as difference of squares.
← Didn't Know|Knew It →
What is $100-4z^2$ factored completely?
What is $100-4z^2$ factored completely?
Tap to reveal answer
$4(5-z)(5+z)$. Factor out GCF of $4$, then recognize difference of squares.
$4(5-z)(5+z)$. Factor out GCF of $4$, then recognize difference of squares.
← Didn't Know|Knew It →
What is $12x^2-27$ factored completely using GCF and structure?
What is $12x^2-27$ factored completely using GCF and structure?
Tap to reveal answer
$3(2x-3)(2x+3)$. Factor out GCF of $3$, then recognize difference of squares.
$3(2x-3)(2x+3)$. Factor out GCF of $3$, then recognize difference of squares.
← Didn't Know|Knew It →
What is $18y^2-8$ factored completely using GCF and structure?
What is $18y^2-8$ factored completely using GCF and structure?
Tap to reveal answer
$2(3y-2)(3y+2)$. Factor out GCF of $2$, then recognize difference of squares.
$2(3y-2)(3y+2)$. Factor out GCF of $2$, then recognize difference of squares.
← Didn't Know|Knew It →
What is $x^2-6x+9$ rewritten as a square?
What is $x^2-6x+9$ rewritten as a square?
Tap to reveal answer
$(x-3)^2$. Recognizes $x^2-2(x)(3)+3^2$ as perfect square trinomial.
$(x-3)^2$. Recognizes $x^2-2(x)(3)+3^2$ as perfect square trinomial.
← Didn't Know|Knew It →
What is $9w^2+24w+16$ rewritten as a square?
What is $9w^2+24w+16$ rewritten as a square?
Tap to reveal answer
$(3w+4)^2$. Recognizes $(3w)^2+2(3w)(4)+4^2$ as perfect square trinomial.
$(3w+4)^2$. Recognizes $(3w)^2+2(3w)(4)+4^2$ as perfect square trinomial.
← Didn't Know|Knew It →
What is $a^4-16$ factored completely over the integers?
What is $a^4-16$ factored completely over the integers?
Tap to reveal answer
$(a-2)(a+2)(a^2+4)$. Factor as $(a^2)^2-4^2$, then apply difference of squares twice.
$(a-2)(a+2)(a^2+4)$. Factor as $(a^2)^2-4^2$, then apply difference of squares twice.
← Didn't Know|Knew It →
What is $81x^4-1$ factored completely over the integers?
What is $81x^4-1$ factored completely over the integers?
Tap to reveal answer
$(3x-1)(3x+1)(9x^2+1)$. Factor as $(9x^2)^2-1^2$, then apply difference of squares twice.
$(3x-1)(3x+1)(9x^2+1)$. Factor as $(9x^2)^2-1^2$, then apply difference of squares twice.
← Didn't Know|Knew It →
What structure suggests factoring by grouping in a $4$-term polynomial?
What structure suggests factoring by grouping in a $4$-term polynomial?
Tap to reveal answer
Two pairs of terms with a common binomial factor. Group terms in pairs to reveal a common binomial factor.
Two pairs of terms with a common binomial factor. Group terms in pairs to reveal a common binomial factor.
← Didn't Know|Knew It →
What common factor should you look for first when rewriting a polynomial expression?
What common factor should you look for first when rewriting a polynomial expression?
Tap to reveal answer
Greatest common factor (GCF). Always factor out common terms before applying other patterns.
Greatest common factor (GCF). Always factor out common terms before applying other patterns.
← Didn't Know|Knew It →
What is the factoring pattern for a difference of cubes $a^3-b^3$?
What is the factoring pattern for a difference of cubes $a^3-b^3$?
Tap to reveal answer
$a^3-b^3=(a-b)(a^2+ab+b^2)$. Standard formula for difference of two perfect cubes.
$a^3-b^3=(a-b)(a^2+ab+b^2)$. Standard formula for difference of two perfect cubes.
← Didn't Know|Knew It →
What is the factoring pattern for a sum of cubes $a^3+b^3$?
What is the factoring pattern for a sum of cubes $a^3+b^3$?
Tap to reveal answer
$a^3+b^3=(a+b)(a^2-ab+b^2)$. Standard formula for sum of two perfect cubes.
$a^3+b^3=(a+b)(a^2-ab+b^2)$. Standard formula for sum of two perfect cubes.
← Didn't Know|Knew It →
What is the factoring pattern for a perfect square trinomial $a^2-2ab+b^2$?
What is the factoring pattern for a perfect square trinomial $a^2-2ab+b^2$?
Tap to reveal answer
$a^2-2ab+b^2=(a-b)^2$. First term squared minus twice the product plus second term squared.
$a^2-2ab+b^2=(a-b)^2$. First term squared minus twice the product plus second term squared.
← Didn't Know|Knew It →
What is the factoring pattern for a perfect square trinomial $a^2+2ab+b^2$?
What is the factoring pattern for a perfect square trinomial $a^2+2ab+b^2$?
Tap to reveal answer
$a^2+2ab+b^2=(a+b)^2$. First term squared plus twice the product plus second term squared.
$a^2+2ab+b^2=(a+b)^2$. First term squared plus twice the product plus second term squared.
← Didn't Know|Knew It →