Question

Multiply: (a) $-3y(5y^2+8y-7)$

(b)$4x^2{y}^2(3x^2-5xy+3y^2)$

Short answer

$$\begin{gathered} \left(a\right)Bymultiplythebinomialsu\sin gthedistributiveproperty,weget \\ -3y(5y^2+8y-7) \\ -15y^3-24y^2+21y \\ \left(b\right)Bymultiplythebinomialsu\sin gthedistributiveproperty,weget \\ 4x^2{y}^2(3x^2-5xy+3y^2) \\ 12x^4{y}^2-20x^3{y}^3+12x^2{y}^4 \end{gathered}$$

Step-by-step solution

Step 1

Given Information:

$$\begin{gathered} \left(a\right)-3y(5y^2+8y-7) \\ \left(b\right)4x^2{y}^2(3x^2-5xy+3y^2) \end{gathered}$$

Step 2

Distributive Property

Distributive Property is an algebraic property that is used to multiply a single value and two or more values within a set of parenthesis.

Step 3Part(a) Step 1. Multiply the binomials

(a)$-3y(5y^2+8y-7)$

Using Distributive property $-3y\times 5y^2+(-3y)\times 8y+(-3y)\times (-7)$

Multiply $-15y^3-24y^2+21y$

Step 4Part(b) Step1. Multiply the binomials

(b)$4x^2{y}^2(3x^2-5xy+3y^{2)}$

Using Distributive property $4x^2{y}^2\times 3x^2+4x^2{y}^2\times (-5xy)+4x^2{y}^2\times 3y^2$

Multiply $12x^4{y}^2-20x^3{y}^3+12x^2{y}^4$