MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Identity (x+y)(x-y)

Prove that. x...

Question

Prove that.
(x+y)³+(y+z)³+(z+x)³ —3(x+y)(y+z)(z+x)=2(x³+y³+z³—3xyz)

Open in App

Solution

LHS=[X³+Y³+3XY(X+Y)]+[Y³+Z³+3YZ(Y+Z)]+[Z³+X³+3ZX(Z+X)]-3XYZ-3X²Y-3XZ²-3X²Z-3Y²Z-3Y²X-3YZ²-3XYZ
=X³+Y³+3X²Y+3XY²+Y³+Z³+3Y²Z+3YZ²+Z³+X³+3Z²X+3X²Z-3XYZ-3X²Y-3XZ²-3X²Z-3Y²Z-3Y²X-3YZ²-3XYZ
=2X³+2Y³+2Z³-6XYZ
=2(X³+Y³+Z³-3XYZ)
LHS=RHS
HENCE PROVED

Suggest Corrections

thumbs-up

77

Similar questions

Q. Prove that:

(x + y)³+ (y + z)³+ (z + x)³ − 3(x + y) (y + z) (z + x) = (x³ + y³ + z³ − 3xyz).

Q. State True or False.

(x - y)^{3} + (y - z)^{3} + (z - x)^{3} =

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

\frac{(x - y)^{3} + {(y - z)}^{3} + {(z - x)}^{3}}{9 (x - y) (y - z) (z - x)} = ?

Q. The value of

\frac{{(x - y)}^{3} + {(y - z)}^{3} + {(z - x)}^{3}}{(x - y) (y - z) (z - x)}

Q. What is the value of the expression

\frac{{(x - y)}^{3} + {(y - z)}^{3} + {(z - x)}^{3}}{(x - y) (y - z) (z - x)}

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Algebraic Identities

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Identity (x+y)(x-y)

Standard IX Mathematics

Join BYJU'S Learning Program

CrossIcon