factorise (2x^2y+5z)^2
Answers
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.
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