Question

factors of 4x²-y²+z²-4xy-2yz+4zx​

Answer 1

The factors of $\bf 4x^2+y^2+z^2-4xy-2yz+4zx$ are $\bf \red{(2x-y+z)(2x-y+z)}$

Given:

$4x^2+y^2+z^2-4xy-2yz+4zx$

To find:

Factors of given polynomial.

Solution:

Identity used:

$\bf (a+b+c)^2=a^2+b^2+b^2+2ab+2bc+2ac$

Step 1:

Write the given polynomial in terms of standard identity.

$(2x)^2+(-y)^2+z^2+2(2x)(-y)+2(-y)z+2(2x)z$

Step 2:

Compare the given polynomial with standard identity.

$a^2=4x^2$

Thus,

a=2x

$2ab= -4xy$

Thus,

b=-y

$c^2=z^2$

Thus,

c=z

Step 3:

Identity which can be written is $(2x-y+z)^2$

Thus,

Factors of given polynomial are $\bf (2x-y+z)(2x-y+z)$.

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