Question

Factors of 9x² + 4y² + 16z² + 12xy -16yz -24xz

Answer 1

Answer:

    (3x - 2y - 4z)²

Step-by-step explanation:

Note that

• (a+b+c)² = a² + b² + c² + 2ab + 2bc + 2ca

Changing a couple of the signs, this becomes

• (a-b-c)² = a² + b² + c² + 2ab - 2bc - 2ca

Now that looks very much like what we have, since the first three terms are actually squares:  9x² = (3x)²,  4y² = (2y)²  and  16z² = (4z)².  So we try this out, putting a=3x, b=2y, c=4z:

    (3x - 2y - 4z)²

= 9x² + 4y² + 16z² + 2(3x)(2y) - 2(2y)(4z) - 2(4z)(3x)

= 9x² + 4y² + 16z² + 12xy - 16yz - 24xz

which is exactly what is given.

So the factorisation is just

    (3x - 2y - 4z)²

Hope this helps!

Answer 2

ANSWER

9x² + 4y² + 16z² + 12xy - 16yz - 24 xz

is similar to identity

=》 (a+b-c)² = a² + b² + c² + 2ab - 2bc - 2ac

So,

By comparing question to equation

a = 3x

b = 2y

c = 4z

(x+y-z)²= (3x)² + (2y)² + (4z)² + 2×(3x × 2y) - 2×(2y×4z) - 2×( 4z × 3x )

So, the solution of the question =

(3x + 2y - 4z)²

Hope, it helps you

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