Example

3(r+2s)=2t-4
a⋅(b-2)=3b
3(r+2s)=2t-4
a⋅(b-2)=3b

Question

$$625a^{4}-25cb^{4}; (25a^{2})^{2}-(16b^{2})^{2}$$

Answer

$$625*a^4-25*c*b^4;(25*a^2)^2-256*b^4$$

Solution


Use Multiplication Distributive Property: \({(xy)}^{a}={x}^{a}{y}^{a}\).
\[\begin{aligned}&625{a}^{4}-25c{b}^{4}\\&{(25{a}^{2})}^{2}-{16}^{2}{({b}^{2})}^{2}\end{aligned}\]
Simplify  \({16}^{2}\)  to  \(256\).
\[\begin{aligned}&625{a}^{4}-25c{b}^{4}\\&{(25{a}^{2})}^{2}-256{({b}^{2})}^{2}\end{aligned}\]
Use Power Rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[\begin{aligned}&625{a}^{4}-25c{b}^{4}\\&{(25{a}^{2})}^{2}-256{b}^{4}\end{aligned}\]
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