Question

What is the standard form of `y= (5x+3)^3+(7x-13)^2`?

Answer 1

`(5x+3)^3+(7x-13)^2 = 125x^3+274x^2-47x+196`

Explanation:

In general we have:

`(a+b)^2 = a^2+2ab+b^2`

`(a+b)^3 = a^3+3a^2b+3ab^2+b^3`

So:

`(7x-13)^2 = (7x)^2-2(7x)(13)+13^2`

`color(white)((7x-13)^2) = 49x^2-182x+169`

`(5x+3)^3 = (5x)^3+3(5x)^2(3)+3(5x)(3^2)+3^3`

`color(white)((5x+3)^3) = 125x^3+225x^2+135x+27`

So:

`(5x+3)^3+(7x-13)^2`

`= 125x^3+225x^2+135x+27 + 49x^2-182x+169`

`= 125x^3+(225+49)x^2+(135-182)x+(27+169)`

`= 125x^3+274x^2-47x+196`