Question

Write each binomial as a product. 0.01x^16-0.16

Answer 1

`0.01x^(16)~~ - ~~0.16 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ 0.01x^(16)\implies \cfrac{001}{100}x^(16)\implies \cfrac{x^(16)}{100}\implies \cfrac{x^(8\cdot 2)}{10^2}\implies \cfrac{(x^8)^2}{10^2}\implies \left( \cfrac{x^8}{10} \right)^2 \\\\[-0.35em] ~\dotfill\\\\ 0.16\implies \cfrac{016}{100}\implies \cfrac{4}{25}\implies \cfrac{2^2}{5^2}\implies \left( \cfrac{2}{5} \right)^2 \\\\[-0.35em] \rule{34em}{0.25pt}`

`\underset{ \textit{difference of squares} }{\left( \cfrac{x^8}{10} \right)^2~~ - ~~\left( \cfrac{2}{5} \right)^2}\implies \left(\cfrac{x^8}{10}-\cfrac{2}{5} \right)\left(\cfrac{x^8}{10}+\cfrac{2}{5} \right)`