Question

Find each product. 1. 2x(x^2-6x+3) 2. 2a^2(5b^2 + 3ab + 6a + 1)

Answer 1

Given:

The expressions are:

$2x(x^2-6x+3)$

$2a^2(5b^2+3ab+6a+1)$

To find:

The product of each expression.

Solution:

According to the distributive property of multiplication over addition, we get

$a(b+c)=ab+ac$

The first expression is:

$2x(x^2-6x+3)$

Using distributive property of multiplication over addition, we get

$2x(x^2-6x+3)=(2x)(x^2)+(2x)(-6x)+(2x)(3)$

$2x(x^2-6x+3)=2x^3-12x^2+6x$

Therefore, the product of $2x(x^2-6x+3)$ is $2x^3-12x^2+6x$.

The second expression is:

$2a^2(5b^2+3ab+6a+1)$

Using distributive property of multiplication over addition, we get

$2a^2(5b^2+3ab+6a+1)=(2a^2)(5b^2)+(2a^2)(3ab)+(2a^2)(6a)+(2a^2)(1)$

$2a^2(5b^2+3ab+6a+1)=10a^2b^2+6a^3b+12a^3+2a^2$

Therefore, the product of $2a^2(5b^2+3ab+6a+1)$ is $10a^2b^2+6a^3b+12a^3+2a^2$.