Answer:
We conclude that:
[tex]25a^2-0.01b^{10}=\left(5a+0.1b^5\right)\left(5a-0.1b^5\right)[/tex]
Step-by-step explanation:
Given the expression
[tex]25a^2-0.01b^{10}[/tex]
Rewrite [tex]25a^2-0.01b^{10}[/tex] as [tex]\left(5a\right)^2-\left(\sqrt{0.01}b^5\right)^2[/tex]
so
[tex]25a^2-0.01b^{10}=\left(5a\right)^2-\left(\sqrt{0.01}b^5\right)^2[/tex]
Apply difference of two squares formulas:
[tex]x^2-y^2=\left(x+y\right)\left(x-y\right)[/tex]
so
[tex]\left(5a\right)^2-\left(\sqrt{0.01}b^5\right)^2=\left(5a+\sqrt{0.01}b^5\right)\left(5a-\sqrt{0.01}b^5\right)[/tex]
[tex]=\left(5a+0.1b^5\right)\left(5a-0.1b^5\right)[/tex] ∵ [tex]\sqrt{0.01}=0.1[/tex],
Therefore, we conclude that:
[tex]25a^2-0.01b^{10}=\left(5a+0.1b^5\right)\left(5a-0.1b^5\right)[/tex]
