Question

question 5 of 9
rewrite without parentheses:
$-6v^{3}(-3v^{2}+6v+8)$
simplify your answer as much as possible.

question 6 of 9
multiply:
$(5b+1)(4b+7)$
simplify your answer.

question 7 of 9
multiply:
$(9u+7v)(9u-7v)$
simplify your answer.

question 8 of 9
rewrite without parentheses and simplify:
$(y-2)^{2}$

question 9 of 9
multiply:
$(3x-4y-3)(4x+5y+1)$
simplify your answer.

Explanation:

Question 5

Step1: Distribute $-6v^3$ to each term

$-6v^3 \times (-3v^2) + (-6v^3) \times 6v + (-6v^3) \times 8$

Step2: Calculate each product

$18v^{3+2} - 36v^{3+1} - 48v^3$

Step3: Simplify exponents

$18v^5 - 36v^4 - 48v^3$

Question 6

Step1: Use FOIL method to multiply

$5b \times 4b + 5b \times 7 + 1 \times 4b + 1 \times 7$

Step2: Calculate each product

$20b^2 + 35b + 4b + 7$

Step3: Combine like terms

$20b^2 + 39b + 7$

Question 7

Step1: Apply difference of squares formula

$(9u)^2 - (7v)^2$

Step2: Calculate each square

$81u^2 - 49v^2$

Question 8

Step1: Expand using square of difference

$(y-2)(y-2) = y \times y + y \times (-2) + (-2) \times y + (-2) \times (-2)$

Step2: Calculate each product

$y^2 - 2y - 2y + 4$

Step3: Combine like terms

$y^2 - 4y + 4$

Question 9

Step1: Distribute each term in first polynomial

$3y \times (4y+5y+1) -4y \times (4y+5y+1) -3 \times (4y+5y+1)$

Step2: Simplify inside parentheses first

$3y \times (9y+1) -4y \times (9y+1) -3 \times (9y+1)$

Step3: Distribute each term

$27y^2 + 3y - 36y^2 -4y -27y -3$

Step4: Combine like terms

$(27y^2-36y^2)+(3y-4y-27y)-3$

Step5: Simplify each group

$-9y^2 -28y -3$

Answer:

1. $18v^5 - 36v^4 - 48v^3$
2. $20b^2 + 39b + 7$
3. $81u^2 - 49v^2$
4. $y^2 - 4y + 4$
5. $-9y^2 -28y -3$