Multiply:
(i) x² + y² + z² − xy + xz + yz by x + y − z

(ii) x² + 4y² + z³ + 2xy + xz − 2yz by x − 2y − z

(iii) x²+ 4y² + 2xy − 3x + 6y + 9 by x − 2y + 3

(iv) 9x² + 25y² + 15xy + 12x − 20y + 16 by 3x − 5y + 4

(v) x²+ 4y² + z² + 2xy + xz – 2yz by (−z + x – 2y)

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Solution

(v) x²+ 4y² + z² + 2xy + xz – 2yz by (−z + x – 2y)

$(x^{2} + 4 y^{2} + z^{2} + 2 x y + x z - 2 y z) (- z + x - 2 y) = (- z) (x^{2} + 4 y^{2} + z^{2} + 2 x y + x z - 2 y z) + (x) (x^{2} + 4 y^{2} + z^{2} + 2 x y + x z - 2 y z) + (- 2 y) (x^{2} + 4 y^{2} + z^{2} + 2 x y + x z - 2 y z) = - x^{2} z - 4 y^{2} z - z^{3} - 2 x y z - x z^{2} + 2 y z^{2} + x^{3} + 4 x y^{2} + x z^{2} + 2 x^{2} y + x^{2} z - 2 x y z - 2 x^{2} y - 8 y^{3} - 2 y z^{2} - 4 x y^{2} - 2 x y z + 4 y^{2} z = x^{3} - 8 y^{3} - z^{3} - x^{2} z + 2 x^{2} y + x^{2} z - 2 x^{2} y - 4 y^{2} z + 4 x y^{2} - 4 x y^{2} + 4 y^{2} z - x z^{2} + 2 y z^{2} + x z^{2} - 2 y z^{2} - 2 x y z - 2 x y z - 2 x y z = x^{3} - 8 y^{3} - z^{3} - 6 x y z$

Hence, the required value is $x^{3} - 8 y^{3} - z^{3} - 6 x y z .$

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Similar questions

(i) $x^{2} + y^{2} + z^{2} - x y + x + y z by x + y - z$

(ii) $x^{2} + 4 y^{2} + z^{2} + 2 x y + x z - 2 y z by x - 2 y - z$

(iii) $x^{2} + 4 y^{2} + 2 x y - 3 x + 6 y + 9 by x - 2 y + 3$

(iv) $9 x^{2} + 25 y^{2} + 15 x y + 2 x - 20 y + 16 by 3 x - 5 y + 4$

Multiply: x²+4y²+z²+2xy+xz-2yz by x-2y-z

(x^{2} + 4 y^{2} + z^{2} + 2 x y + x z - 2 y z) b y (- z + x - 2 y .)

(x^{2} + 4 y^{2} + z^{2} + 2 x y + x z - 2 y z) b y (- z + x - 2 y .)

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

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