Question

Multiply : (a)$4x^2(2x^2-3x+5)$

(b)$-6a^{3}b(3a^2-2ab+6b^2)$

Short answer

$$\begin{gathered} \left(a\right)Bymultiplythebinomialsu\sin gDistributiveproperty,weget \\ 4x^2(2x^2-3x+5) \\ 8x^4-12x^3+20x^2 \\ \left(b\right)Bymultiplythebinomialsu\sin gdistributiveproperty,weget \\ -6a^{3}b(3a^2-2ab+6b^2) \\ -18a^{5}b+12a^4{b}^2-36a^3{b}^3 \end{gathered}$$

Step-by-step solution

Step 1

Given Information:

(a) $4x^2(2x^2-3x+5)$

(b) $-6a^{3}b(3a^2-2ab+6b^2)$

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) Step1. Multiply the binomials

(a)$4x^2(2x^2-3x+5)$

Distribute:$4x^2\times 2x^2+4x^2\times (-3x)+4x^2\times 5$

Multiply:$8x^4-12x^3+20x^2$

Step 4Part(b) Step1. Multiply the binomials

(b)$-6a^{3}b(3a^2-2ab+6b^2)$

Distribute:$-6a^{3}b\times 3a^2+(-6a^{3}b)\times (-2ab)+(-6a^{3}b)\times 6b^2$

Multiply:$-18a^{5}b+12a^4{b}^2-36a^3{b}^3$