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Algebraic Identities

Factorise x -...

Question

Factorise x - y + z - 1 + 2y - 2xz

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x^{2} + 2 y^{2} + 8 z^{2} + 2 \sqrt{2} x y - 8 y z - 4 \sqrt{2} x z

Q. Factorise the following:

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

Q. The number of solutions

(x, y, z)

to the system of equations

x + 2 y + 4 z = 9, 4 y z + 2 x z + x y = 13, x y z = 3

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are integers is

Q. Factorise the expression.

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

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{(x + y + z - 3)}^{3} - {(x - 1)}^{3} - {(y - 1)}^{3} - {(z - 1)}^{3}

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