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`.