Question

Type the correct answer in each box. Use numerals instead of words.

Simplify the following polynomial expression.

(5x^2+13x-4)-(17x^2+7x-19)+(5x-7)(3x+1)


____x^2-____x+_____

Answer 1

3x² - 10x + 8

Explanation:

Given

|(5x² + 13x - 4) - (17x² + 7x - 19) + (5x - 7)(3x + 1)

Expanding (5x - 7)(3x + 1)

Each term in the second factor is multiplied by each term in the first factor

5x(3x + 1) - 7(3x + 1) ← distribute both parenthesis

= 15x² + 5x - 21x - 7 ← collect like terms

= 15x² - 16x - 7

Expression can now be expressed as

(5x² + 13x - 4) - (17x² + 7x - 19) + (15x² - 16x - 7)

Distribute parenthesis

= 5x² + 13x - 4 - 17x² - 7x + 19 + 15x² - 16x - 7 ← collect like terms

= 3x² - 10x + 8

Answer 2

3x^2-10x+8.

Explanation:

(5x^2+13x-4)-(17x^2+7x-19)+(5x-7)(3x+1) Removing the parentheses:

= 5x^2+13x-4-17x^2-7x+19+ 15x^2+5x-21x-7 bringing like terms together:

= 5x^2-17x^2+15x^2+13x-7x-21x+5x-4+19-7

= 3x^2-10x+8