# Question #49a3a

Jan 29, 2018

$55 {a}^{2} + 24 a - 16$

#### Explanation:

If I understood you correctly you mean
${\left(7 a + a\right)}^{2} - {\left(- 4 + 3 a\right)}^{2}$
otherwise feel free to correct me.
1. Calculate $7 a + a$

$7 a + a = 8 a$

1. Square the brackets using the binomial formula

${\left(a + b\right)}^{2} = {a}^{2} + 2 a b + {b}^{2}$

${\left(8 a\right)}^{2} - {\left(3 a - 4\right)}^{2} = {8}^{2} {a}^{2} - \left({3}^{2} {a}^{2} - 4 \cdot 3 \cdot 2 a + {4}^{2}\right)$

1. Simplify

${8}^{2} {a}^{2} - \left({3}^{2} {a}^{2} - 4 \cdot 3 \cdot 2 a + {4}^{2}\right) = 64 {a}^{2} - 9 {a}^{2} + 24 a - 16 = 55 {a}^{2} + 24 a - 16$

Jan 29, 2018

$- 2 {a}^{2} + 7 a + 4$

#### Explanation:

In the absence of any formatting, the meaning of the question is not clear. Here is another interpretation which I think is more likely because there is nothing to indicate that the given powers are for the whole expressions.

We have: second expression minus the first expression:

$\left(7 a + {a}^{2}\right) \textcolor{b l u e}{- \left(- 4 + 3 {a}^{2}\right)}$

$= 7 a + {a}^{2} \textcolor{b l u e}{+ 4 - 3 {a}^{2}} \text{ } \leftarrow$ multiply out the bracket

$= - 2 {a}^{2} + 7 a + 4 \text{ } \leftarrow$ simplify the like terms.