Question

factorize 25x^2+4y^2+9z^2-20xy-12yz+30xz

Answer 1

heya mate here is your answer

using identity (a+b+c)² we can solve this

(-5x)² + (2y)² + (-3z)² + 2×(-5x)(2y) + 2× 2y×(-3z) +2 × (-3z)(-5x)

= (-5x + 2y -3z)²

= (-5x + 2y -3z)(-5x +2y -3z)

hope it helps you

Answer 2

Factors of$\bf 25 {x}^{2} + 4 {y}^{2} + 9 {z}^{2} - 20xy - 12yz + 30xz$ are $\bf\red{( 5x - 2y + 3z)(5x-2y+3z)}$.

Given:

• $25 {x}^{2} + 4 {y}^{2} + 9 {z}^{2} - 20xy - 12yz + 30xz$

To find:

• Factorize the polynomial.

Solution:

Identity to be used:

• $\bf ( {a + b + c)}^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2ab + 2bc + 2ca$

Step 1:

Rewrite the given polynomial.

To identify the negative sign; search common term in both negative numbers.

y is common in both, so y is having negative sign.

${(5x)}^{2} + {( - 2y)}^{2} + {(3z)}^{2} + 2(5x)( - 2y) + 2( - 2y)(3z) + 2(5x)(3z)$

Step 2:

Write the values of a,b, and c .

On comparison with identity

$a = 5x$

$b = - 2y$

and

$c = 3z$

so,

$25 {x}^{2} + 4 {y}^{2} + 9 {z}^{2} - 20xy - 12yz + 30xz = ( {5x - 2y + 3z)}^{2}$

Thus,

Factors of $\bf 25 {x}^{2} + 4 {y}^{2} + 9 {z}^{2} - 20xy - 12yz + 30xz$ are $\bf( 5x - 2y + 3z)(5x-2y+3z)$.

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