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Expansion of (x+y+z)^2

Find the prod...

Question

Find the product :
$(2 x - y + 3 z) (4 x^{2} + y^{2} + 9 z^{2} + 2 x y + 3 y z - 6 x z)$

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Solution

$= (2 x - y + 3 z) (4 x^{2} + y^{2} + {9 z}^{2} + 2 x y + 3 y z - 6 x z) = (a + b + c) (a^{2} + b^{2} + c^{2} - a b - b c - a c) = a^{3} + b^{3} + c^{3} - 3 a b c = {(2 x)}^{3} + {(- y)}^{3} + {(3 z)}^{3} - 3. (2 x) (- y) (3 z) = {8 x}^{3} - y^{3} + 27 z^{3} + 18 x y z$

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Similar questions

Q. Question 35
Find the following product:

(2 x - y + 3 z) (4 x^{2} + y^{2} + 9 z^{2} + 2 x y + 3 y z - 6 x z)

Q. Question 35
Find the following product:

(2 x - y + 3 z) (4 x^{2} + y^{2} + 9 z^{2} + 2 x y + 3 y z - 6 x z)

Q. Solve the following equations :

2 x y - 4 x + y = 17, 3 y z + y - 6 z = 52, 6 x z + 3 z + 2 x = 29.

(x + 2 y + 3 z)^{2}

using algebraic identity.

Q. Solve the following equations:

x^{2} + y^{2} - z^{2} = 21

,

3 x z + 3 y z - 2 x y = 18

,

x + y - z = 5

.

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