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प्रश्न
Simplify:
(5x − 3)(x + 2) − (2x + 5)(4x − 3)
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उत्तर
To simplify, we will proceed as follows:
\[\left( 5x - 3 \right)\left( x + 2 \right) - \left( 2x + 5 \right)\left( 4x - 3 \right)\]
\[ = \left[ \left( 5x - 3 \right)\left( x + 2 \right) \right] - \left[ \left( 2x + 5 \right)\left( 4x - 3 \right) \right]\]
\[= \left[ 5x\left( x + 2 \right) - 3\left( x + 2 \right) \right] - \left[ 2x\left( 4x - 3 \right) + 5\left( 4x - 3 \right) \right]\] (Distributive law)
\[= 5 x^2 + 10x - 3x - 6 - 8 x^2 + 6x - 20x + 15\]
\[= 5 x^2 - 8 x^2 + 10x - 3x + 6x - 20x - 6 + 15\] (Rearranging)
\[= 5 x^2 - 8 x^2 + 10x - 3x + 6x - 20x - 6 + 15\]
\[ = - 3 x^2 - 7x + 9\] (Combining like terms)
Hence, the answer is \[- 3 x^2 - 7x + 9\].
संबंधित प्रश्न
Find each of the following product: \[\left( \frac{7}{9}a b^2 \right) \times \left( \frac{15}{7}a c^2 b \right) \times \left( - \frac{3}{5} a^2 c \right)\]
Express each of the following product as a monomials and verify the result in each case for x = 1:
(x2)3 × (2x) × (−4x) × (5)
Simplify: a(b − c) + b(c − a) + c(a − b)
Simplify: \[\frac{3}{2} x^2 ( x^2 - 1) + \frac{1}{4} x^2 ( x^2 + x) - \frac{3}{4}x( x^3 - 1)\]
Simplify: a2b(a3 − a + 1) − ab(a4 − 2a2 + 2a) − b (a3 − a2 − 1)
Multiply:
(2x + 8) by (x − 3)
Multiply: \[\left( - \frac{a}{7} + \frac{a^2}{9} \right)by\left( \frac{b}{2} - \frac{b^2}{3} \right)\].
Simplify:
(5x + 3)(x − 1)(3x − 2)
Simplify:
(3x − 2)(2x − 3) + (5x − 3)(x + 1)
Multiply:
23xy2 × 4yz2
