Property 5
Difference of Two Squares
\(a^2-b^2=\left(a-b\right)\left(a+b\right)\)
Factorize the following expressions to determine their simplest form.
1.
\(x^2-y^2=?\)
2.
\(x^2-9=?\)
3.
\(a^2-4b^2=?\)
4.
\(\samefrac{16a^2-9b^2}{4a+3b}=?\)
5.
\(\samefrac{102^2-100^2}{51^2-50^2}=?\)
6.
\(\samefrac{x^2+5x+6}{x^2-4}=?\)
7.
\(\samefrac{a^2-9}{a^2-2a-3}:\samefrac{a+3}{2a+2}=?\)
8.
\(\samefrac{x^2-25}{x^2+7x+10}:\samefrac{x^2-7x+10}{x^2-4}=?\)
9.
\(\left(2^x-1\right)\left(2^x+1\right)\left(2^{2x}+1\right)\left(2^{4x}+1\right)=2^{32}-1\)
\(\Rightarrow x=?\)
10.
\(\samefrac{a-\samefrac4a}{a-2}\cdot\samefrac{a^2}{a^2+2a}=?\)
11.
\(\samefrac{a^2+a-b^2-b}{a+b+1}=?\)
12.
\(\left(2a+1\right)^2-\left(a-1\right)^2=?\)
13.
\(x\cdot y\in\mathbb Z^+\)
\(x^2-y^2=19\)
\(\Rightarrow x=?\)
14.
\(x\cdot y\in\mathbb Z^+\)
\(x^2-y^2=-7\)
\(\Rightarrow x=?\)
15.
\(\sqrt{2005\cdot1995+25}=?\)