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प्रश्न
Simplify:
(3x + 2y)(4x + 3y) − (2x − y)(7x − 3y)
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उत्तर
To simplify, we will proceed as follows:
\[\left( 3x + 2y \right)\left( 4x + 3y \right) - \left( 2x - y \right)\left( 7x - 3y \right)\]
\[ = \left[ \left( 3x + 2y \right)\left( 4x + 3y \right) \right] - \left[ \left( 2x - y \right)\left( 7x - 3y \right) \right]\]
\[= \left[ 3x\left( 4x + 3y \right) + 2y\left( 4x + 3y \right) \right] - \left[ 2x\left( 7x - 3y \right) - y\left( 7x - 3y \right) \right]\] (Distributive law)
\[= 12 x^2 + 9xy + 8xy + 6 y^2 - \left[ 14 x^2 - 6xy - 7xy + 3 y^2 \right]\]
\[ = 12 x^2 + 9xy + 8xy + 6 y^2 - 14 x^2 + 6xy + 7xy - 3 y^2\]
\[= 12 x^2 - 14 x^2 + 9xy + 8xy + 6xy + 7xy + 6 y^2 - 3 y^2\] (Rearranging)
\[= - 2 x^2 + 30xy + 3 y^2\] (Combining like terms)
Thus, the answer is \[- 2 x^2 + 30xy + 3 y^2\].
संबंधित प्रश्न
Find each of the following product:
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Find each of the following product:
(7ab) × (−5ab2c) × (6abc2)
Find each of the following product:
\[\left( - \frac{2}{7} a^4 \right) \times \left( - \frac{3}{4} a^2 b \right) \times \left( - \frac{14}{5} b^2 \right)\]
Express each of the following product as a monomials and verify the result in each case for x = 1:
(x2)3 × (2x) × (−4x) × (5)
Evaluate each of the following when x = 2, y = −1.
\[\left( \frac{3}{5} x^2 y \right) \times \left( - \frac{15}{4}x y^2 \right) \times \left( \frac{7}{9} x^2 y^2 \right)\]
Find the following product: \[- \frac{8}{27}xyz\left( \frac{3}{2}xy z^2 - \frac{9}{4}x y^2 z^3 \right)\]
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(x6 − y6) by (x2 + y2)
Simplify:
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Simplify:
(x3 − 2x2 + 3x − 4) (x −1) − (2x − 3)(x2 − x + 1)
Simplify : (2x − 1)(2x + 1)(4x2 + 1)(16x4 + 1)
