Question

Factorize :

x2+4xy+4y2-9z2

Answer 1

Answer:

x^2+4xy+4y^2-9z^2

=x^2+2*2x*2y+(2y)^2-(3y)^2

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

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

Answer 2

Question:-

Factorize:

x² + 4xy + 4y² - 9z²

Solution:-

[(x)² + (2×2x×y) + (2y)²] - (3z)²

= (x+2y)² - (3z)² [Identity used (a+b)²]

= (x+2y-3z) (x+2y+3z) [Identity used a²-b²]

Identity to be remembered:-

▪︎(a+b)² = a²+2ab+b²

▪︎(a-b)² = a²-2ab+b²

▪︎a² - b² = (a-b)(a+b)