Question

How do you combine like terms in `(6x ^ { 2} + 2x - 9) + ( 8x ^ { 2} - 5x + 1) - ( 3x - 4) ( 7x + 2)`?

Answer 1

`(6x^2+2x-9)+(8x^2-5x+1)-(3x-4)(7x+2)=color(blue)(-7x^2+19x`

Explanation:

`(6x^2+2x-9)+(8x^2-5x+1)-(3x-4)(7x+2)`

First expand `(3x-4)(7x+2)` using the FOIL method.

`(3x*7x)+(3x*2)+(-4*7x)+(-4*2)`

Simplify.

`21x^2+6x-28x-8`

`21x^2-22x-8`

Return the expanded expression to the original expression.

`(6x^2+2x-9)+(8x^2-5x+1)-(21x^2-22x-8)`

Distribute the negative sign (-1).

`(6x^2+2x-9)+(8x^2-5x+1)+(-21x^2+22x+8)`

Gather like terms.

`(6x^2+8x^2-21x^2)+(2x-5x+22x)+(-9+1+8)`

Combine like terms.

`-7x^2+19x+0`

`-7x^2+19x`