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Question
Factorise the following by taking out the common factors:
(mx + ny)2 + (nx - my)2
Solution
(mx + ny)2 + (nx - my)2
= m2x2 + n2y2 + 2mnxy + n2x2 + m2y2 - 2mnxy
= m2x2 + n2y2 + n2x2 + m2y2
= m2x2 + n2x2 + m2y2 + n2y2
= x2(m2 + n2) + y2(m2 + n2)
Here, the common factor is (m2 + n2).
Dividing throughout by (m2 + n2), we get
`(x^2("m"^2 + "n"^2))/(("m"^2 + "n"^2)) + (y^2("m"^2 + "n"^2))/(("m"^2 + "n"^2)`
= x2 + y2
∴ (mx + ny)2 + (nx - my)2
= (m2 + n2)(x2 + y2).
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