Home
Class 9
MATHS
Verify : (i) x^3+y^3=(x+y)(x^2-x y+y^2) ...

Verify : (i) `x^3+y^3=(x+y)(x^2-x y+y^2)` (ii) `x^3-y^3=(x-y)(x^2+x y+y^2)`

Text Solution

AI Generated Solution

To verify the identities given in the question, we will approach each part step by step. ### Part (i): Verify \( x^3 + y^3 = (x + y)(x^2 - xy + y^2) \) **Step 1: Start with the left-hand side (LHS)** \[ LHS = x^3 + y^3 \] ...
Promotional Banner

Similar Questions

Explore conceptually related problems

Simplify: (x+y)^3-(x-y)^3-6y(x^2-y^2)

"(2x+3y)^3-(2x-3y)^3

The factors of x^3-x^2y-x y^2+y^3 are (a (x+y)(x^2-x y+y^2) (b) (x+y)(x^2+x y+y^2) (c) (x+y)^2(x-y) (d) (x-y)^2(x+y)

Simplify: (2x+3y)(3x+4y)-(7x+3y)(x+2y)

(x^3+3x y^2)dx+(y^3+3x^2y)dy=0

Add: (i) x y^2+4x^2y-7x^2y-3x y^2+3\ a n d\ x^2y+x y^2 (ii) 5x^2+7y-6z^2,\ 4y+3x^2,9x^2+2z^2-9y\ a n d\ 2y-2x^2

If (x^(2) + y^(2))/(x^(2) - y^(2)) = 2(1)/(8) , find : (i) (x)/(y) (ii) (x^(3) + y^(3))/(x^(3) - y^(3))

Simplify: (3x+2y)(4x+3y)-\ (2x-y)(7x-3y)

Divide: (i) x+2x^2+3x^4-x^5\ by 2x , (ii) y^4-3y^3+1/2y^2\ by 3y