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Question
Simplify:
\[\frac{m^2 - n^2}{\left( m + n \right)^2} \times \frac{m^2 + mn + n^2}{m^3 - n^3}\]
Solution
We know that,
a3 + b3 = (a + b)(a2 − ab + b2)
a3 − b3 = (a − b)(a2 + ab + b2)
a2 − b2= (a + b) (a − b)
\[\frac{m^2 - n^2}{\left( m + n \right)^2} \times \frac{m^2 + mn + n^2}{m^3 - n^3}\]
\[ = \frac{\left( m + n \right)\left( m - n \right)}{\left( m + n \right)\left( m + n \right)} \times \frac{\left( m^2 + mn + n^2 \right)}{\left( m - n \right)\left( m^2 + mn + n^2 \right)}\]
\[= \frac{1}{m + n}\]
RELATED QUESTIONS
Simplify:
\[\frac{a^2 + 10a + 21}{a^2 + 6a - 7} \times \frac{a^2 - 1}{a + 3}\]
Simplify:
\[\frac{4 x^2 - 11x + 6}{16 x^2 - 9}\]
Simplify:
\[\frac{1 - 2x + x^2}{1 - x^3} \times \frac{1 + x + x^2}{1 + x}\]
Factorise:
27m3 − 216n3
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125y3 − 1
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343a3 − 512b3
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(3a + 5b)3 − (3a − 5b)3
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(a + b)3 − a3 − b3
Factorise: 27p3 - 125q3.
Simplify: (2x + 3y)3 - (2x - 3y)3
