Question

find the product.
4x^{2}(6x^{3}+5x^{2}-6x + 2)

4x^{2}(6x^{3}+5x^{2}-6x + 2)=square. (simplify your answer.)

Explanation:

Step1: Apply distributive property

$4x^{2}(6x^{3}+5x^{2}-6x + 2)=4x^{2}\times6x^{3}+4x^{2}\times5x^{2}-4x^{2}\times6x+4x^{2}\times2$

Step2: Use exponent - product rule $a^{m}\times a^{n}=a^{m + n}$

$4x^{2}\times6x^{3}=(4\times6)x^{2 + 3}=24x^{5}$, $4x^{2}\times5x^{2}=(4\times5)x^{2+2}=20x^{4}$, $4x^{2}\times6x=(4\times6)x^{2 + 1}=24x^{3}$, $4x^{2}\times2 = 8x^{2}$

Step3: Combine results

$24x^{5}+20x^{4}-24x^{3}+8x^{2}$

Answer:

$24x^{5}+20x^{4}-24x^{3}+8x^{2}$