# 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)

Jun 1, 2018

$\rightarrow {\left(3 x + 4\right)}^{2} - \left(x + 7\right) \left(x - 6\right)$

$= {\left(3 x\right)}^{2} + 2 \cdot \left(3 x\right) \cdot 4 + {4}^{2} + \left(x + 7\right) \left(x + 6\right)$

$= 9 {x}^{2} + 24 x + 16 + x \left(x + 6\right) + 7 \left(x + 6\right)$

$= 9 {x}^{2} + 24 x + 16 + {x}^{2} + 6 x + 7 x + 42$

$= 10 {x}^{2} + 37 x + 58$

Jun 1, 2018

$\textcolor{b l u e}{26 - 25 x - 10 {x}^{2}}$

#### Explanation:

Bracket the two products leaving the negation out side:

$- \left[{\left(3 x + 4\right)}^{2}\right] - \left[\left(x + 7\right) \left(x - 6\right)\right]$

Expand inside the square brackets:

${\left(3 x + 4\right)}^{2} = \left(3 x + 4\right) \left(3 x + 4\right) = 9 {x}^{2} + 24 x + 16$

$\left(x + 7\right) \left(x - 6\right) = {x}^{2} + 7 x - 6 x - 42 = {x}^{2} + x - 42$

Now put these back in the square brackets:

$- \left[9 {x}^{2} + 24 x + 16\right] - \left[{x}^{2} + x - 42\right]$

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

$- 9 {x}^{2} - 24 x - 16 - {x}^{2} - x + 42$

$- 10 {x}^{2} - 25 x + 26$

It is best practice to express this as:

$26 - 25 x - 10 {x}^{2}$

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

Negations before brackets often catch students out.

Hope this helps.