Question

Help with this question, keep getting it wrong - (3x+4)² - (x+7)(x-6) ?

Expand and simplify:
(3x+4)² - (x+7)(x-6)

Answer 1

`rarr(3x+4)^2-(x+7)(x-6)`

`=(3x)^2+2*(3x)*4+4^2+(x+7)(x+6)`

`=9x^2+24x+16+x(x+6)+7(x+6)`

`=9x^2+24x+16+x^2+6x+7x+42`

`=10x^2+37x+58`

Answer 2

`color(blue)(26-25x-10x^2)`

Explanation:

Bracket the two products leaving the negation out side:

`-[(3x+4)^2]-[(x+7)(x-6)]`

Expand inside the square brackets:

`(3x+4)^2=(3x+4)(3x+4)=9x^2+24x+16`

`(x+7)(x-6)=x^2+7x-6x-42=x^2+x-42`

Now put these back in the square brackets:

`-[9x^2+24x+16]-[x^2+x-42]`

Multiply inside the brackets by the negation, then remove brackets and simplify:

`-9x^2-24x-16-x^2-x+42`

`-10x^2-25x+26`

It is best practice to express this as:

`26-25x-10x^2`

This ensures that you do not lose negations when doing further calculations.

Negations before brackets often catch students out.

Hope this helps.