How do I find the square of a binomial?

Oct 20, 2014

Finding the square of a binomial can be done by using the Distributive Property or FOIL. FOIL stands for First, Outer, Inner, Last. There also is a definition in which ${\left(a + b\right)}^{2} = {a}^{2} + 2 a b + {b}^{2}$ or ${\left(a - b\right)}^{2} = {a}^{2} - 2 a b + {b}^{2}$

Example:
${\left(4 x + 3\right)}^{2}$
$\left(4 x + 3\right) \left(4 x + 3\right)$

Distributive Property:
$4 x \left(4 x + 3\right) + 3 \left(4 x + 3\right)$
$16 {x}^{2} + 12 x + 12 x + 9$
$16 {x}^{2} + 24 x + 9$ (Proves the ${a}^{2} + 2 a b + {b}^{2}$)

FOIL:
$\left(4 x + 3\right) \left(4 x + 3\right)$
F: 4x4x
O: 4x
3
I: 34x
L: 3
3
$4 x \cdot 4 x + 4 x \cdot 3 + 3 \cdot 4 x + 3 \cdot 3$
$16 {x}^{2} + 12 x + 12 x + 9$
$16 {x}^{2} + 24 x + 9$