# How do you multiply (7x+3) (7x+3)?

Aug 21, 2015

$\left(7 x + 3\right) \left(7 x + 3\right) = {\left(7 x + 3\right)}^{2} = 49 {x}^{2} + 42 x + 9$

#### Explanation:

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

${\left(7 x + 3\right)}^{2}$ is the square of a sum with the form ${\left(a + b\right)}^{2} = {a}^{2} + 2 a b + {b}^{2}$, where $a = 7 x$ and $b = 3$.

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

${\left(7 x + 3\right)}^{2} = 49 {x}^{2} + 42 x + 9$

You could also use the FOIL method.

$\left(7 x + 3\right) \left(7 x + 3\right) = \left(7 x \cdot 7 x\right) + \left(7 x \cdot 3\right) + \left(3 \cdot 7 x\right) + \left(3 \cdot 3\right)$$=$

$\left(7 x + 3\right) \left(7 x + 3\right) = 49 {x}^{2} + 21 x + 21 x + 9$$=$

$\left(7 x + 3\right) \left(7 x + 3\right) = 49 {x}^{2} + 42 x + 9$