Question:
Factorize each of the following algebraic expressions:
−4(x − 2y)2 + 8(x −2y)
Solution:
$-4(x-2 y)^{2}+8(x-2 y)$
$=[-4(x-2 y)+8](x-2 y) \quad[$ Taking $(x-2 y)$ as the common factor $]$
$=4[-(x-2 y)+2](x-2 y) \quad\{$ Taking 4 as the common factor of $[-4(x-2 y)+8]\}$
$=4(2 y-x+2)(x-2 y)$
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