Simplify the expression a²\;b^4\;-\;b²\;a^4/ab(a\;+\;b)

Correct Answer is : ab2−a2bab² - a²bab2−a2b

Correct Answer is : ab2−a2bab² - a²bab2−a2b

Test Index

WAEC Mathematics 2017 Paper

Question : 26

Total: 49

\frac{a^2\;b^4\;-\;b^2\;a^4}{ab(a\;+\;b)}

Solution:

Concept:

Factorise the numerator and cancel common terms with the denominator.

Explanation:

Write the numerator by taking

a^2b^2

common.

a^2b^4 - b^2a^4 = a^2b^2(b^2 - a^2)

Use the difference of squares:

b^2 - a^2 = (b-a)(b+a)

So the expression becomes:

\frac{a^2b^2(b-a)(b+a)}{ab(a+b)}

Cancel

ab

and

(a+b)

= ab(b-a)

Expand:

ab(b-a) = ab^2 - a^2b

Answer:

D.\; ab^2 - a^2b

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