Question

Write as a product: 25a2−0.01b10

Answer 1

Answer:

We conclude that:

$25a^2-0.01b^{10}=\left(5a+0.1b^5\right)\left(5a-0.1b^5\right)$

Step-by-step explanation:

Given the expression

$25a^2-0.01b^{10}$

Rewrite $25a^2-0.01b^{10}$ as $\left(5a\right)^2-\left(\sqrt{0.01}b^5\right)^2$

so

$25a^2-0.01b^{10}=\left(5a\right)^2-\left(\sqrt{0.01}b^5\right)^2$

Apply difference of two squares formulas:

$x^2-y^2=\left(x+y\right)\left(x-y\right)$

so

$\left(5a\right)^2-\left(\sqrt{0.01}b^5\right)^2=\left(5a+\sqrt{0.01}b^5\right)\left(5a-\sqrt{0.01}b^5\right)$

                               $=\left(5a+0.1b^5\right)\left(5a-0.1b^5\right)$    ∵ $\sqrt{0.01}=0.1$,

Therefore, we conclude that:

$25a^2-0.01b^{10}=\left(5a+0.1b^5\right)\left(5a-0.1b^5\right)$