Question

Factorize 3x^2+4y^2+25z^2-4√3xy-20yz+10√3zx

Answer 1

Step-by-step explanation:

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Answer 2

Given,

An algebraic expression: 3x^2+4y^2+25z^2-4√3xy-20yz+10√3zx

To find,

The factorized product of the given expression.

Solution,

We can simply solve this mathematical problem using the following process:

Mathematically,

If a, b, and c are three numbers, then, there exists an algebraic identity such that;

(a+b+c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca

{Statement-1}

Now, according to the question;

On simplifying the given expression, we get;

3x^2+4y^2+25z^2-4√3xy-20yz+10√3zx

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

= {(√3x) + (-2y) + (5z)}^2

{according to statement-1}

= {√3x - 2y + 5z}^2

= (√3x - 2y + 5z)(√3x - 2y + 5z)

Hence, the factorized product of the given expression is equal to (√3x - 2y + 5z)(√3x - 2y + 5z).