# What is the standard form of a polynomial (5h + 4)(3h + 6) ?

$\left(5 h + 4\right) \left(3 h + 6\right) = 15 {h}^{2} + 42 h + 24$

#### Explanation:

$\left(5 h + 4\right) \left(3 h + 6\right) = 5 h \left(3 h + 6\right) + 4 \left(3 h + 6\right)$
$= 5 h \times 3 h + 5 h \times 6 + 4 \times 3 h + 4 \times 6$
$= 5 \times 3 \times h \times h + 5 \times 6 \times h + 4 \times 3 \times h + 4 \times 6$
$5 \times 3 = 15$
$h \times h = {h}^{2}$
$5 \times 3 \times h \times h = 15 {h}^{2}$
$5 \times 6 = 30$
$5 \times 6 \times h = 30 h$
$4 \times 3 = 12$
$4 \times 3 \times h = 12 h$
$4 \times 6 = 24$
$5 \times 3 \times h \times h + 5 \times 6 \times h + 4 \times 3 \times h + 4 \times 6$
$= 15 {h}^{2} + 30 h + 12 h + 24$
$30 h + 12 h = 42 h$
$15 {h}^{2} + 30 h + 12 h + 24 = 15 {h}^{2} + 42 h + 24$
Thus,
$\left(5 h + 4\right) \left(3 h + 6\right) = 15 {h}^{2} + 42 h + 24$