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प्रश्न
Find the following product: \[- \frac{4}{27}xyz\left( \frac{9}{2} x^2 yz - \frac{3}{4}xy z^2 \right)\]
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उत्तर
To find the product, we will use distributive law as follows:
\[- \frac{4}{27}xyz\left( \frac{9}{2} x^2 yz - \frac{3}{4}xy z^2 \right)\]
\[ = \left\{ \left( - \frac{4}{27}xyz \right)\left( \frac{9}{2} x^2 yz \right) \right\} - \left\{ \left( - \frac{4}{27}xyz \right)\left( \frac{3}{4}xy z^2 \right) \right\}\]
\[ = \left\{ \left( - \frac{4}{27} \times \frac{9}{2} \right)\left( x^{1 + 2} y^{1 + 1} z^{1 + 1} \right) \right\} - \left\{ \left( - \frac{4}{27} \times \frac{3}{4} \right)\left( x^{1 + 1} y^{1 + 1} z^{1 + 2} \right) \right\}\]
\[ = \left\{ \left( - \frac{4^2}{{27}_3} \times \frac{9}{2} \right)\left( x^{1 + 2} y^{1 + 1} z^{1 + 1} \right) \right\} - \left\{ \left( - \frac{4^1}{{27}_9} \times \frac{3}{4} \right)\left( x^{1 + 1} y^{1 + 1} z^{1 + 2} \right) \right\}\]
\[ = - \frac{2}{3} x^3 y^2 z^2 + \frac{1}{9} x^2 y^2 z^3\]
Thus, the answer is \[- \frac{2}{3} x^3 y^2 z^2 + \frac{1}{9} x^2 y^2 z^3\].
संबंधित प्रश्न
Find each of the following product:
\[\left( - \frac{1}{27} a^2 b^2 \right) \times \left( \frac{9}{2} a^3 b^2 c^2 \right)\]
Find each of the following product: \[( - 7xy) \times \left( \frac{1}{4} x^2 yz \right)\]
Find each of the following product: \[\left( \frac{4}{3} u^2 vw \right) \times \left( - 5uv w^2 \right) \times \left( \frac{1}{3} v^2 wu \right)\]
Evaluate each of the following when x = 2, y = −1.
\[\left( \frac{3}{5} x^2 y \right) \times \left( - \frac{15}{4}x y^2 \right) \times \left( \frac{7}{9} x^2 y^2 \right)\]
Simplify: a(b − c) − b(c − a) − c(a − b)
Simplify: \[\frac{3}{2} x^2 ( x^2 - 1) + \frac{1}{4} x^2 ( x^2 + x) - \frac{3}{4}x( x^3 - 1)\]
Multiply:
(7x + y) by (x + 5y)
Find the following product and verify the result for x = − 1, y = − 2: \[\left( \frac{1}{3}x - \frac{y^2}{5} \right)\left( \frac{1}{3}x + \frac{y^2}{5} \right)\]
Simplify:
(x2 − 3x + 2)(5x − 2) − (3x2 + 4x − 5)(2x − 1)
Simplify : (m2 − n2m)2 + 2m3n2
