Multiply Factored Expressions - International Brotherhood of Electrical Workers Exam IBEW

1. What is the product when you expand $(3x+2)^2$?

   $9x^2+12x+4$. Applies the binomial square pattern $(a+b)^2 = a^2 + 2ab + b^2$, with $a=3x$ and $b=2$.

2. What is the product when you expand $(x-3)(x^2+3x+9)$?

   $x^3-27$. Applies the difference of cubes formula $(a-b)(a^2 + ab + b^2) = a^3 - b^3$, with $a=x$ and $b=3$.

3. What is the product when you expand $(2x+1)(x+4)$?

   $2x^2+9x+4$. Uses FOIL distribution on the binomials, combining to a quadratic with all positive coefficients.

4. What is the product when you expand $(x-4)(x+6)$?

   $x^2+2x-24$. Employs the FOIL method on the binomials, resulting in a quadratic with positive linear and negative constant terms.

5. What is the product when you expand $(x-5)(x-2)$?

   $x^2-7x+10$. Multiplies the binomials using FOIL, yielding a quadratic with negative linear and positive constant terms.

6. What is the product when you expand $(3x-2)(2x+7)$?

   $6x^2+17x-14$. Applies FOIL to multiply the binomials, combining terms to form a quadratic with positive coefficients except the constant.

7. What is the product when you expand $(x-8)^2$?

   $x^2-16x+64$. Expands the square of the binomial with the pattern $(a-b)^2 = a^2 - 2ab + b^2$, for $a=x$ and $b=8$.

8. What is the product when you expand $(2x-1)^2$?

   $4x^2-4x+1$. Expands using the square formula $(a-b)^2 = a^2 - 2ab + b^2$, where $a=2x$ and $b=1$.

9. What is the product when you expand $(x+7)(2x-3)$?

   $2x^2+11x-21$. Distributes via FOIL, combining terms to form a quadratic with positive leading and linear coefficients.

10. What is the product when you expand $(x+4)(x-4)$?

    $x^2-16$. Recognizes the difference of squares formula $(a+b)(a-b) = a^2 - b^2$, with $a=x$ and $b=4$.

11. What is the product when you expand $(2x+5)(2x-5)$?

    $4x^2-25$. Utilizes the difference of squares pattern $(a+b)(a-b) = a^2 - b^2$, where $a=2x$ and $b=5$.

12. What is the product when you expand $(2x+3)(x-5)$?

    $2x^2-7x-15$. Distributes each term using FOIL, yielding a quadratic with a negative linear coefficient and constant.

13. What is the product when you expand $(5-x)(5+x)$?

    $25-x^2$. Employs the difference of squares formula $(a-b)(a+b) = a^2 - b^2$, with $a=5$ and $b=x$.

14. What is the product when you expand $4x(2x-7)$?

    $8x^2-28x$. Multiplies the monomial $4x$ by each term in the binomial, resulting in a quadratic expression.

15. What is the product when you expand $-3(x-2)$?

    $-3x+6$. Distributes the scalar $-3$ to each term in the binomial, flipping signs appropriately.

16. What is the product when you expand $-2x(3x+5)$?

    $-6x^2-10x$. Distributes $-2x$ across the binomial, producing negative coefficients for both terms.

17. What is the product when you expand $a(b+c)$?

    $ab+ac$. Applies the distributive property by multiplying $a$ by each term inside the parentheses to expand the expression.

18. What is the product when you expand $(x+2)(x^2+2x+4)$?

    $x^3+4x^2+8x+8$. Distributes the linear factor across the quadratic, combining like terms to form a cubic polynomial.

19. What is the product when you expand $(x+3)(x+5)$?

    $x^2+8x+15$. Uses the FOIL method to multiply the binomials, combining like terms for the quadratic expression.

20. What is the product when you expand $(x-1)(x^2+x+1)$?

    $x^3-1$. Uses the difference of cubes formula $(a-b)(a^2 + ab + b^2) = a^3 - b^3$, for $a=x$ and $b=1$.

21. What is the product when you expand $(4x-3)(x+2)$?

    $4x^2+5x-6$. Applies FOIL to the binomials, resulting in a quadratic with a positive linear term and negative constant.

22. What is the product when you expand $(x+9)^2$?

    $x^2+18x+81$. Squares the binomial using the formula $(a+b)^2 = a^2 + 2ab + b^2$, where $a=x$ and $b=9$.

23. What is the product when you expand $(x+1)(x^2-x+1)$?

    $x^3+1$. Follows the sum of cubes pattern $(a+b)(a^2 - ab + b^2) = a^3 + b^3$, for $a=x$ and $b=1$.

Study these flashcards