Factor the expression completely. a4b2+ab5

Question

Factor the expression completely.  a4b2+ab5

Neelam Wainwright · Accepted Answer

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 ,
$a^{2} - b^{2} = a + b a - b$
$a^{3} + b^{3} = a + b a^{2} - a b + b^{2}$
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
$a^{4} b^{2} + a b^{5} = a b^{2} a^{3} + b^{3} = a b^{2} a + b a^{2} - a b + b^{2}$
Hence the factor form of the expression is $a^{4} b^{2} + a b^{5} = a b^{2} a + b a^{2} - a b + b^{2} .$

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

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