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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:
\[\left( - \frac{7}{5}x y^2 z \right) \times \left( \frac{13}{3} x^2 y z^2 \right)\]
Find each of the following product: \[\left( \frac{7}{9}a b^2 \right) \times \left( \frac{15}{7}a c^2 b \right) \times \left( - \frac{3}{5} a^2 c \right)\]
Evaluate each of the following when x = 2, y = −1.
\[(2xy) \times \left( \frac{x^2 y}{4} \right) \times \left( x^2 \right) \times \left( y^2 \right)\]
Simplify: a(b − c) − b(c − a) − c(a − b)
Simplify: x2(x2 + 1) − x3(x + 1) − x(x3 − x)
Multiply:
(5x + 3) by (7x + 2)
Multiply:
(2x2 − 1) by (4x3 + 5x2)
Simplify:
a2b2(a + 2b)(3a + b)
Multiply:
(12a + 17b) × 4c
Solve the following equation.
2(x − 4) = 4x + 2
