Question

Complete.(a) The binomial 25x2 - 16 is in the form o? - b2, where a =and b =(b) Use the formula a2 - b2 = (a + b)(a - b) to factor 25x2 - 16.25x2 - 16 =

Answer 1

Given expression is

$25x^2-16$

It can be written as

$(5x)^2-(4)^2$

Comparing with the form

$a^2-b^2$

The values of a and b are

$\begin{gathered} a=5x \\ b=4 \end{gathered}$

Now, it is known that

$a^2-b^2=(a+b)(a-b)$

Therefore,

$\begin{gathered} 25x^2-16=(5x)^2-(4)^2 \\ =(5x+4)(5x-4) \end{gathered}$