Example

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

Question

$$6 { \times }^{ 2 } { y }^{ 2 } -12 { \times }^{ 2 } { y }^{ 2 } + { \times }^{ 2 } { y }^{ 2 } =$$

Answer

$$-6*^3*y^2+^2*y^2$$

Solution


Remove parentheses.
\[6{}^{2}{y}^{2}-12{}^{2}{y}^{2}+{}^{2}{y}^{2}\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[6{}^{3}{y}^{2}-12{}^{2}{y}^{2}+{}^{2}{y}^{2}\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[6{}^{3}{y}^{2}-12{}^{3}{y}^{2}+{}^{2}{y}^{2}\]
Simplify  \({}^{2}{y}^{2}\)  to  \({y}^{2}{}^{2}\).
\[6{}^{3}{y}^{2}-12{}^{3}{y}^{2}+{y}^{2}{}^{2}\]
Regroup terms.
\[6{}^{3}{y}^{2}-12{}^{3}{y}^{2}+{}^{2}{y}^{2}\]
Collect like terms.
\[(6{}^{3}{y}^{2}-12{}^{3}{y}^{2})+{}^{2}{y}^{2}\]
Simplify.
\[-6{}^{3}{y}^{2}+{}^{2}{y}^{2}\]
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