Question

Write as a product: 25a2−0.01b10

Answer 1

We conclude that:

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

Explanation:

Given the expression

`25a^2-0.01b^(10)`

Rewrite
`25a^2-0.01b^(10)` as
`\left(5a\right)^2-\left(√(0.01)b^5\right)^2`

so

`25a^2-0.01b^(10)=\left(5a\right)^2-\left(√(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(√(0.01)b^5\right)^2=\left(5a+√(0.01)b^5\right)\left(5a-√(0.01)b^5\right)`

`=\left(5a+0.1b^5\right)\left(5a-0.1b^5\right)` ∵
`√(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)`