Factorize
$25 x^{2} + 16 y^{2} + 4 z^{2} - 40 x y + 16 y z - 20 x z$

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Solution

$25 x^{2} + 16 y^{2} + 4 z^{2} - 40 x y + 16 y z - 20 x z$
$=$ $(- 5 x)^{2} + (4 y)^{2} + (2 z)^{2} + 2 (- 5 x) (4 y) + 2 (4 y) (2 z) + 2 (- 5 x) (2 z)$
Suitable identities is $(x + y + z)^{2} = x^{2} + y^{2} + z^{2} + 2 x y + 2 y z + 2 x z$
Therefore, $(- 5 x)^{2} + (4 y)^{2} + (2 z)^{2} + 2 (- 5 x) (4 y) + 2 (4 y) (2 z) + 2 (- 5 x) (2 z)$
$=$ $(- 5 x + 4 y + 2 z)^{2}$

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25 x^{2} + 16 y^{2} + 4 z^{2} + 40 x y + 16 y z + 20 x z

Question 29
Factorise the following:

9 x^{2} + 4 y^{2} + 16 z^{2} + 12 x y - 16 y z - 24 x z

25 x^{2} + 16 y^{2} + 4 z^{2} - 40 x y + 16 y z - 20 x z

16 x^{2} + 4 y^{2} + 9 z^{2} - 16 x y - 12 y z + 24 x z

Question 29
Factorise the following:

9 x^{2} + 4 y^{2} + 16 z^{2} + 12 x y - 16 y z - 24 x z

25 x^{2} + 16 y^{2} + 4 z^{2} - 40 x y + 16 y z - 20 x z

16 x^{2} + 4 y^{2} + 9 z^{2} - 16 x y - 12 y z + 24 x z

25 x^{2} + 16 y^{2} + 40 x y

x = 1

y = - 1

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