Multiply:

$9 x^{2} + 25 y^{2} + 15 x y - 12 x + 20 y + 16$
by $3 x - 5 y + 4$

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Solution

To multiply: $9 x^{2} + 25 y^{2} + 15 x y - 12 x + 20 y + 16$

by $3 x - 5 y + 4$

$∴ (3 x - 5 y + 4) \times (9 x^{2} + 25 y^{2} + 15 x y - 12 x + 20 y + 16)$

$= (3 x - 5 y + 4) \times (9 x^{2} + 25 y^{2} + 16 + 15 x y + 20 y - 12 x)$

$= (3 x - 5 y + 4) \times [(3 x)^{2} + (- 5 y)^{2} + (4)^{2}$

$- 3 x \times (- 5 y) - (- 5 y) \times (4) - (3 x) \times (4)]$

$= (3 x)^{3} + (- 5 y)^{3} + (4)^{3} - 3 \times 3 x \times (- 5 y) \times (4)$

$[∵ (a + b + c) (a^{2} + b^{2} + c^{2} - a b - b c - c a) = a^{3} + b^{3} + c^{3} - 3 a b c]$

$= 27 x^{3} - 125 y^{3} + 64 + 180 x y$

Hence, $27 x^{3} - 125 y^{3} + 64 + 180 x y$ is the required result.

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(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 9x²+25y²+15xy+12x-20y+16 by 3x-5y-4 using suitable identity

9 x^{2} + 25 y^{2} = 181 a n d x y = - 6

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