Factor the expression completely. a^{4} b^{2}+ab^{5}

Factor the expression completely.
${a}^{4}{b}^{2}+a{b}^{5}$
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Step 1
We can factor the expression by taking the greatest common factors out from the expression . The common factors are the variable expression or constant number which are presented in both the terms of the expression .
We can also use the algebraic formulas to write the factor form of the expression . We can use the formulas ,
${a}^{2}-{b}^{2}=a+ba-b$
${a}^{3}+{b}^{3}=a+b{a}^{2}-ab+{b}^{2}$
Step 2
Consider the expression ${a}^{4}{b}^{2}+a{b}^{5}$.
Both the terms in the expressions are the multiples of a,b
The term ${a}^{4}{b}^{2}=a.a.a.a.b.b$
The term $a{b}^{5}=a.b.b.b.b.b$ { a.b.b is common in both the terms }
We have the common factor $a{b}^{2}$, take the common factor out and simplify the expression ${a}^{4}{b}^{2}+a{b}^{5}$, we get
${a}^{4}{b}^{2}+a{b}^{5}=a{b}^{2}{a}^{3}+{b}^{3}=a{b}^{2}a+b{a}^{2}-ab+{b}^{2}$
Hence the factor form of the expression is ${a}^{4}{b}^{2}+a{b}^{5}=a{b}^{2}a+b{a}^{2}-ab+{b}^{2}.$