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)

2 Answers
Jun 1, 2018

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

Jun 1, 2018

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.