Question

algebraic identities

Answer 1

(64m²-144mn+81n²)-25p²
⇒{(8m)²-2(8m)(9n)+(9n)²}- (5p)²
⇒(8m-9n)² - (5p)²              [using identity (a-b)²= a²-2ab+b²)]
⇒(8m-9n+5p)(8m-9n-5p)          [using identity a²-b²=(a+b)(a-b)]


hope it helps you! :)

Answer 2

Answer:

(a + b)² = a² + 2ab + b²

(a - b)² = a² - 2ab + b²

a² - b² = (a + b) (a - b)

(x + a) (x + b) = x² + ( a+b)x + ab

$(x+y+z)^{2} = x^{2} + y^{2} + z^{2} + 2xy + 2zy + 2zx$

$(x+y)^{3} = x^{3} + y^{3} + 3xy(x+y)$

$(x-y)^{3} = x^{3} - y^{3} - 3xy(x-y)$

$x^{3} + y^{3} + z^{3} - 3xyz = (x+y+z)(x^{2}+y^{2}+z^{2}-xy-yz-zx )$

Step-by-step explanation: