Question

How do you simplify `2( 4x - 5) + 5( - 2x + 3)` as a binomial?

Answer 1

`5-2x` or `5(1-(2x)/5)^1`

Explanation:

`2(4x-5)+5(-2x+3) = 8x-10-10x+15`

`=-2x+5 =5-2x`

If you want to get this in the other binomial form of `a(1+bx)^n` we must divide both sides by 5:
`5(1-(2x)/5)^1`

This can be proved as `(a+bx)^n=a^n(1+(bx)/a)^n`

For `n=1` we get:
`a^n(1+(bx)/a)^1=a^1(1+(bx)/a)=a(1+1((bx)/a))=a(1+(bx)/a)`