Algebra 2 Flashcards: Using Structure To Rewrite Expressions

What this deck covers

This deck focuses on Using Structure To Rewrite Expressions, giving you a quick way to review the definitions, rules, and examples that matter most for Algebra 2.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: What is $6a^2b+9ab^2$ rewritten by factoring out the GCF?

Answer: $3ab(2a+3b)$. Factor out common term $3ab$.

Flashcard 2: What is $x^2-6x+9$ rewritten as a square?

Answer: $(x-3)^2$. Recognizes $x^2-2(x)(3)+3^2$ as perfect square trinomial.

Flashcard 3: What is the factoring pattern for a perfect square trinomial $a^2-2ab+b^2$?

Answer: $a^2-2ab+b^2=(a-b)^2$. First term squared minus twice the product plus second term squared.

Flashcard 4: What is $2x^2+8x$ rewritten by factoring out the GCF?

Answer: $2x(x+4)$. Factor out common term $2x$.

Flashcard 5: What is $x^2-9y^2$ factored using structure?

Answer: $(x-3y)(x+3y)$. Recognizes $x^2-(3y)^2$ as difference of squares.

Flashcard 6: What is the factoring pattern for a difference of squares $a^2-b^2$?

Answer: $a^2-b^2=(a-b)(a+b)$. Standard pattern for difference of two perfect squares.

Flashcard 7: What is $x^3+y^3$ factored using structure?

Answer: $(x+y)(x^2-xy+y^2)$. Standard sum of cubes formula.

Flashcard 8: What is $9x^2-25$ factored using structure?

Answer: $(3x-5)(3x+5)$. Recognizes $(3x)^2-5^2$ as difference of squares.

Flashcard 9: What is $8x^3-1$ factored using structure?

Answer: $(2x-1)(4x^2+2x+1)$. Recognizes $(2x)^3-1^3$ and applies difference of cubes formula.

Flashcard 10: What is $16a^2b^2-81$ factored using structure?

Answer: $(4ab-9)(4ab+9)$. Recognizes $(4ab)^2-9^2$ as difference of squares.

Flashcard 11: What is $x^4-2x^2+1$ rewritten using structure?

Answer: $(x^2-1)^2$. Recognizes $(x^2)^2-2(x^2)(1)+1^2$ as perfect square trinomial.

Flashcard 12: What is $9w^2+24w+16$ rewritten as a square?

Answer: $(3w+4)^2$. Recognizes $(3w)^2+2(3w)(4)+4^2$ as perfect square trinomial.

Flashcard 13: What is $x^2+2xy+y^2$ rewritten using structure?

Answer: $(x+y)^2$. Standard perfect square trinomial pattern.

Flashcard 14: What is $x^2+7x+12$ factored using structure?

Answer: $(x+3)(x+4)$. Find two numbers that multiply to $12$ and add to $7$: $3$ and $4$.

Flashcard 15: What is $x^3+8$ factored using structure?

Answer: $(x+2)(x^2-2x+4)$. Recognizes $x^3+2^3$ and applies sum of cubes formula.

Flashcard 16: What is $x^2-5x+6$ factored using structure?

Answer: $(x-2)(x-3)$. Find two numbers that multiply to $6$ and add to $-5$: $-2$ and $-3$.

Flashcard 17: What is $x^4-6x^2+9$ rewritten using structure?

Answer: $(x^2-3)^2$. Recognizes $(x^2)^2-2(x^2)(3)+3^2$ as perfect square trinomial.

Flashcard 18: What is $x^4-9$ factored completely over the integers?

Answer: $(x^2-3)(x^2+3)$. Recognizes $(x^2)^2-3^2$ as difference of squares.

Flashcard 19: What is $x^3-y^3$ factored using structure?

Answer: $(x-y)(x^2+xy+y^2)$. Standard difference of cubes formula.

Flashcard 20: What is $x^2+10x+25$ rewritten as a perfect square?

Answer: $(x+5)^2$. Recognizes $x^2+2(x)(5)+5^2$ as perfect square trinomial.

Flashcard 21: What is $x^2-2xy+y^2$ rewritten using structure?

Answer: $(x-y)^2$. Standard perfect square trinomial pattern.

Flashcard 22: What structure suggests factoring by grouping in a $4$-term polynomial?

Answer: Two pairs of terms with a common binomial factor. Group terms in pairs to reveal a common binomial factor.

Flashcard 23: What is $4x^2-12x+9$ rewritten as a perfect square?

Answer: $(2x-3)^2$. Recognizes $(2x)^2-2(2x)(3)+3^2$ as perfect square trinomial.

Flashcard 24: What is $18y^2-8$ factored completely using GCF and structure?

Answer: $2(3y-2)(3y+2)$. Factor out GCF of $2$, then recognize difference of squares.

Flashcard 25: What is $4x^2-y^2$ factored using structure?

Answer: $(2x-y)(2x+y)$. Recognizes $(2x)^2-y^2$ as difference of squares.

Flashcard 26: What is $25p^2-30p+9$ rewritten as a perfect square?

Answer: $(5p-3)^2$. Recognizes $(5p)^2-2(5p)(3)+3^2$ as perfect square trinomial.

Flashcard 27: What is the factoring pattern for a perfect square trinomial $a^2+2ab+b^2$?

Answer: $a^2+2ab+b^2=(a+b)^2$. First term squared plus twice the product plus second term squared.

Flashcard 28: What is $4x^2+12x+9$ rewritten as a perfect square?

Answer: $(2x+3)^2$. Recognizes $(2x)^2+2(2x)(3)+3^2$ as perfect square trinomial.

Flashcard 29: What is $x^4+2x^2+1$ rewritten using structure?

Answer: $(x^2+1)^2$. Recognizes $(x^2)^2+2(x^2)(1)+1^2$ as perfect square trinomial.

Flashcard 30: Identify the rewrite that shows $x^4-y^4$ as a difference of squares.

Answer: $x^4-y^4=(x^2)^2-(y^2)^2$. Recognizes $x^4$ as $(x^2)^2$ and $y^4$ as $(y^2)^2$.

Flashcard 31: What is $2x^2+7x+3$ factored using structure?

Answer: $(2x+1)(x+3)$. Use factoring by grouping or trial method for quadratic.

Flashcard 32: What is $15x^3y-10x^2y^2$ rewritten by factoring out the GCF?

Answer: $5x^2y(3x-2y)$. Factor out common term $5x^2y$.

Flashcard 33: What is $36m^2-49n^2$ factored using structure?

Answer: $(6m-7n)(6m+7n)$. Recognizes $(6m)^2-(7n)^2$ as difference of squares.

Flashcard 34: What is the factoring pattern for a difference of cubes $a^3-b^3$?

Answer: $a^3-b^3=(a-b)(a^2+ab+b^2)$. Standard formula for difference of two perfect cubes.

Flashcard 35: What is $a^4-16$ factored completely over the integers?

Answer: $(a-2)(a+2)(a^2+4)$. Factor as $(a^2)^2-4^2$, then apply difference of squares twice.

Flashcard 36: What is $x^4-1$ factored completely over the integers?

Answer: $(x-1)(x+1)(x^2+1)$. Factor as $(x^2)^2-1^2$, then apply difference of squares twice.

Flashcard 37: What is $49m^2n^2-1$ factored using structure?

Answer: $(7mn-1)(7mn+1)$. Recognizes $(7mn)^2-1^2$ as difference of squares.

Flashcard 38: What is $81x^4-1$ factored completely over the integers?

Answer: $(3x-1)(3x+1)(9x^2+1)$. Factor as $(9x^2)^2-1^2$, then apply difference of squares twice.

Flashcard 39: What common factor should you look for first when rewriting a polynomial expression?

Answer: Greatest common factor (GCF). Always factor out common terms before applying other patterns.

Flashcard 40: What is $y^2-12y+36$ rewritten as a perfect square?

Answer: $(y-6)^2$. Recognizes $y^2-2(y)(6)+6^2$ as perfect square trinomial.

Flashcard 41: What is $x^4-y^4$ factored completely over the integers?

Answer: $(x-y)(x+y)(x^2+y^2)$. Factor difference of squares twice: $(x^2-y^2)(x^2+y^2) = (x-y)(x+y)(x^2+y^2)$.

Flashcard 42: What is $x^2-y^2$ factored using structure?

Answer: $(x-y)(x+y)$. Standard difference of squares pattern.

Flashcard 43: What is $100-4z^2$ factored completely?

Answer: $4(5-z)(5+z)$. Factor out GCF of $4$, then recognize difference of squares.

Flashcard 44: What is $12x^2-27$ factored completely using GCF and structure?

Answer: $3(2x-3)(2x+3)$. Factor out GCF of $3$, then recognize difference of squares.

Flashcard 45: What is the factoring pattern for a sum of cubes $a^3+b^3$?

Answer: $a^3+b^3=(a+b)(a^2-ab+b^2)$. Standard formula for sum of two perfect cubes.

Flashcard 46: What is $64t^3+125$ factored using structure?

Answer: $(4t+5)(16t^2-20t+25)$. Recognizes $(4t)^3+5^3$ and applies sum of cubes formula.

Flashcard 47: What is $27a^3-b^3$ factored using structure?

Answer: $(3a-b)(9a^2+3ab+b^2)$. Recognizes $(3a)^3-b^3$ and applies difference of cubes formula.

Flashcard 48: What is $x^2-81$ factored using structure?

Answer: $(x-9)(x+9)$. Recognizes $x^2-9^2$ as difference of squares.

Flashcard 49: What is $x^4+6x^2+9$ rewritten using structure?

Answer: $(x^2+3)^2$. Recognizes $(x^2)^2+2(x^2)(3)+3^2$ as perfect square trinomial.