Example

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

Question

$$\frac { a ^ { 2 } + a b } { a ^ { 2 } - b ^ { 2 } } \cdot \frac { a ^ { 3 } - b ^ { 3 } } { a b ( a + b ) } ; U$$

Answer

$$-x-y*a^2+a^3*b-b^2*a^3-b^3*h*a*t*a*b*(a+b);;a^2-2*a*b+b^2;a^3+b^3$$

Solution


Regroup terms.
\[\begin{aligned}&-x-y{a}^{2}+a{a}^{2}b-{b}^{2}{a}^{3}-{b}^{3}hatab(a+b)\\&\\&{a}^{2}-2ab+{b}^{2}\\&{a}^{3}+{b}^{3}\end{aligned}\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[\begin{aligned}&-x-y{a}^{2}+{a}^{1+2}b-{b}^{2}{a}^{3}-{b}^{3}hatab(a+b)\\&\\&{a}^{2}-2ab+{b}^{2}\\&{a}^{3}+{b}^{3}\end{aligned}\]
Simplify  \(1+2\)  to  \(3\).
\[\begin{aligned}&-x-y{a}^{2}+{a}^{3}b-{b}^{2}{a}^{3}-{b}^{3}hatab(a+b)\\&\\&{a}^{2}-2ab+{b}^{2}\\&{a}^{3}+{b}^{3}\end{aligned}\]
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