Simplify (x^2+6x+5)(2x^2-8x+7)

Expert Answers

An illustration of the letter 'A' in a speech bubbles

Multiply each term in the first polynomial by each term in the second polynomial.

`(x^2 * 2x^2 + x^2 * - 8x + x^2 * 7 + 6x * 2x^2 + 6x * -8x + 6x * 7 + 5 * 2x^2 + 5 * -8x + 5 * 7)`


Multiply each term in the first polynomial by each term in the second polynomial.

`(2x^4 + 4x^3 - 31x^2 + 2x + 35)`


Remove the parentheses around the expression `2x^4 + 4x^3 - 31x^2 + 2x + 35`

Therefore, the answer is

`2x^4 + 4x^3 - 31x^2 + 2x + 35`

Approved by eNotes Editorial
An illustration of the letter 'A' in a speech bubbles

The product (x^2+6x+5)(2x^2-8x+7) has to be determined.

(x^2+6x+5)(2x^2-8x+7)

= x^2*(2x^2-8x+7)+6x*(2x^2-8x+7)+5*(2x^2-8x+7)

= 4x^4 - 8x^3 + 7x^2 + 12x^3 - 48x^2 +42x + 10x^2 - 40x + 35

= 4x^4 + 4x^3 - 31x^2 + 2x + 35

The product (x^2+6x+5)(2x^2-8x+7) = 4x^4 + 4x^3 - 31x^2 + 2x + 35

See eNotes Ad-Free

Start your 48-hour free trial to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Get 48 Hours Free Access
Approved by eNotes Editorial