Math, asked by arijitkumar2353, 5 hours ago

factorise (2x^2y+5z)^2​

Answers

Answered by amansharma264
4

EXPLANATION.

Factorizes.

⇒ (2x + 2y + 5z)².

As we know that,

Formula of :

⇒ (x + y + z)² = (x)² + (y)² + (z)² + 2(x)(y) + 2(y)(z) + 2(z)(x).

Using this formula in the equation, we get.

⇒ (2x)² + (2y)² + (5z)² + 2(2x)(2y) + 2(2y)(5z) + 2(5z)(2x).

⇒ 4x² + 4y² + 25z² + 8xy + 20yz + 20zx.

⇒ (2x + 2y + 5z)² = 4x² + 4y² + 25z² + 8xy + 20yz + 20zx.

                                                                                                                         

MORE INFORMATION.

(1) = (x + y)² = x² + y² + 2xy.

(2) = (x - y)² = x² + y² - 2xy.

(3) = (x² - y²) = (x + y)(x - y).

(4) = (x² + y²) = (x + y)² - 2xy.

(5) = (x³ + y³) = (x + y)(x² - xy + y²).

(6) = (x³ - y³) = (x - y)(x² + xy + y²).

(7) = (x + y)³ = x³ + 3x²y + 3xy² + y³.

(8) = (x - y)³ = x³ - 3x²y + 3xy² - y³.

Answered by Anonymous
5

Step-by-step explanation:

As we know that

(x+y+z)² = x²+y²+z²+2xy+2yz+2xz

So,

(2x+2y+5z)²

→(2x)²+(2y)²+(5z)²+(2×2x×2y)+(2×2y×5z)+(2×2x×5z)

→ 4x²+4y²+25z²+8xy+20yz+20zx

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