x(x + z) – y (y + z)
Answer
(i) x(x + z) – y (y + z)
x2 + xz – y2 – yz
Rearrange the above terms we get,
x2 – y2 + xz – yz
We know that, (a2 – b2) = (a + b) (a – b)
So, (x + y) (x – y) + z(x – y)
(x – y) (x + y + z)
(ii) a12x4 – a4x12
a12x4 – a4x12
Take out common in both terms,
a4x4 (a8 – x8)
a4x4((a4)2 – (x4)2)
We know that, (a2 – b2) = (a + b) (a – b)
a4x4 (a4 + x4) (a4 – x4)
a4x4 (a4 + x4) ((a2)2 – (x2)2)
a4x4(a4 + x4) (a2 + x2) (a2 – x2)
a4x4 (a4 + x4) (a2 + x2) (a + x) (a – x)
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