Question

How do you combine like terms in `(5- x ) ( 5+ x ) + ( x - 5) ^ { 2} + ( 2x - 10) ( x + 3)`?

Answer 1

`2x^2-14x+20`

Explanation:

`(5-x)(5+x)+(x-5)^2+(2x-10)(x+3)` can be separated into 3 parts:

• `(5-x)(5+x)=25-x^2` (difference of 2 squares)

• `(x-5)^2=x^2-10x+25` (perfect squares)

• `(2x-10)(x+3)=2x^2-4x-30`

`(5-x)(5+x)+(x-5)^2+(2x-10)(x+3)`
`=25-x^2+x^2-10x+25+2x^2-4x-30`
`=25cancel(-x^2+x^2)-10x+25+2x^2-4x-30`
`=2x^2-14x+20`

Answer 2

`2x^2-14x+20`

Explanation:

`(5-x)(5+x)+(x-5)^2+(2x-10)(x+3)`

=`25-x^2+x^2-10x+25+2x^2-4x-30`

=`2x^2-14x+20`