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प्रश्न
Find the product −3y(xy + y2) and find its value for x = 4 and y = 5.
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उत्तर
To find the product, we will use distributive law as follows:
\[- 3y\left( xy + y^2 \right)\]
\[ = - 3y \times xy + \left( - 3y \right) \times y^2 \]
\[ = - 3x y^{1 + 1} - 3 y^{1 + 2} \]
\[ = - 3x y^2 - 3 y^3\]
Substituting x = 4 and y = 5 in the result, we get:
\[- 3x y^2 - 3 y^3 \]
\[ = - 3\left( 4 \right) \left( 5 \right)^2 - 3 \left( 5 \right)^3 \]
\[ = - 3\left( 4 \right)\left( 25 \right) - 3\left( 125 \right)\]
\[ = - 300 - 375\]
\[ = - 675\]
Thus, the product is ( \[- 3x y^2 - 3 y^3\]), and its value for x = 4 and y = 5 is ( \[-\] 675).
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(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:
(x3 − 2x2 + 3x − 4) (x −1) − (2x − 3)(x2 − x + 1)
Show that: \[\left( \frac{4m}{3} - \frac{3n}{4} \right)^2 + 2mn = \frac{16 m^2}{9} + \frac{9 n^2}{16}\]
What is the result of 2y(3y² − 4y + 5)?
What is the product of (x + 3) and (x − 5)?
