# Question 5e199

Jul 31, 2017

$\text{yes } \left(b - 4\right) \left(b + 4\right)$

#### Explanation:

$\text{a difference of two squares is what it says 2 square numbers}$
$\text{separated by a subtraction}$

$\text{for example}$

$25 = {5}^{2} \text{ and "16=4^2" are two squares}$

$\text{note that } 25 - 16 = 9$

$\text{and } \left(5 - 4\right) \left(5 + 4\right) = 1 \times 9 = 9$

$\text{this is the way they are factorised}$

$\text{in general }$

•color(white)(x)a^2-b^2=(a-b)(a+b)#

$\Rightarrow {b}^{2} - 16 = \left(b - 4\right) \left(b + 4\right)$

Jul 31, 2017

${b}^{2} - 16 = \left(b + 4\right) \left(b - 4\right)$

#### Explanation:

The expression "difference or two squares describes exactly what is involved.

"Difference" means to subtract terms

"Two" there are are TWO terms involved

"Squares" are recognized by:
square numbers and variables with even powers.
(A square number is formed by multiplying a number by itself. )

The squares are: $1 , 4 , 9 , 16 , 25 , 36 , 49 , 64 , 81 , \ldots .$ and so

The difference of squares is factorised as:

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

${b}^{2} \mathmr{and} 16$ are both squares and they are being subtracted.
This is the difference of two squares and can be factorised

${b}^{2} - 16 = \left(b + 4\right) \left(b - 4\right)$