How do you factor #1 - 100x^2#?

1 Answer
Dec 29, 2015

Answer:

Use difference of squares to factorize this. The method is given below.

Explanation:

Difference of squares #a^2 - b^2 = (a-b)(a+b)#

Now let us take up our problem

#1 - 100x^2#

Ask can we write this expression in #a^2-b^2 # form.

#1 is same as 1^2#
#100# can be written as #10^2#

So, we have #1 - 100x^2# as #1^2-10^2x^2#

If #10^2x^2# is putting you off, it is nothing but #(10x)^2#

Rule #(a^mb^m) = (ab)^m#

Now our expression becomes
#1^2 - (10x)^2#

This can be factored by the difference of squares.

#1^2 - (10x)^2 = (1-10x)(1+10x)# Answer