Question

What is the standard form of `y= (2x+3)^2+(3x-14)^2`?

Answer 1

`y=12x^2 + 96x+205`

Explanation:

given`y= color(blue)((2x+3)^2) + color(brown)((3x-14)^2`

Expanding the brackets

In what follows I use brackets only as a means for grouping so that you can see what is hapening
`y= color(blue)((2x^2 +12x+9)) + color(brown)((9x^2 +84x+ 196))`

Grouping like terms:
`y= (2x^2+9x^2) + (12x + 84x) +(9+196)`

`y=12x^2 + 96x+205`