Question

x^2-4xy+4y^2-x-2y-12 factorize

Answer 1

Given to factorise:-

${x}^{2} + 4xy + 4 {y}^{2} - x - 2y - 12$

Solution:-

${x}^{2} + 4xy + 4 {y}^{2} - x - 2y - 12$

$= {(x)}^{2} +( 2 \times x \times 2y) + {(2y)}^{2} - 1(x + 2y) - 12$

$= {(x + 2y)}^{2} - (x + 2y) - 12$

Now, let z=x+2y.

Therefore,${(x + 2y)}^{2} - (x + 2y) - 12$

$= {z}^{2} - z - 12$

$= {z}^{2} - 4z + 3z - 12$

$= z(z - 4) + 3(z - 4)$

$= (z + 3)(z - 4)$

Putting the value of z, we get,

$= (x + 2y + 3)(x + 2y - 4)$

Answer:-

$(x + 2y + 3)(x + 2y - 4)$

Answer 2

Answer:

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