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प्रश्न
Simplify:
(5x + 3)(x − 1)(3x − 2)
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उत्तर
To simplify, we will proceed as follows:
\[\left( 5x + 3 \right)\left( x - 1 \right)\left( 3x - 2 \right)\]
\[ = \left[ \left( 5x + 3 \right)\left( x - 1 \right) \right]\left( 3x - 2 \right)\]
\[= \left[ 5x\left( x - 1 \right) + 3\left( x - 1 \right) \right]\left( 3x - 2 \right)\] (Distributive law)
\[= \left[ 5 x^2 - 5x + 3x - 3 \right]\left( 3x - 2 \right)\]
\[ = \left[ 5 x^2 - 2x - 3 \right]\left( 3x - 2 \right)\]
\[ = 3x\left( 5 x^2 - 2x - 3 \right) - 2\left( 5 x^2 - 2x - 3 \right)\]
\[ = 15 x^3 - 6 x^2 - 9x - \left[ 10 x^2 - 4x - 6 \right]\]
\[ = 15 x^3 - 6 x^2 - 9x - 10 x^2 + 4x + 6\]
\[= 15 x^3 - 6 x^2 - 10 x^2 - 9x + 4x + 6\] (Rearranging)
\[= 15 x^3 - 16 x^2 - 5x + 6\] (Combining like terms)
Thus, the answer is \[15 x^3 - 16 x^2 - 5x + 6\].
संबंधित प्रश्न
Find each of the following product:
(−5a) × (−10a2) × (−2a3)
Find each of the following product:
(−4x2) × (−6xy2) × (−3yz2)
Find each of the following product: \[\left( \frac{7}{9}a b^2 \right) \times \left( \frac{15}{7}a c^2 b \right) \times \left( - \frac{3}{5} a^2 c \right)\]
Find each of the following product: \[\left( \frac{4}{3} u^2 vw \right) \times \left( - 5uv w^2 \right) \times \left( \frac{1}{3} v^2 wu \right)\]
Express each of the following product as a monomials and verify the result in each case for x = 1:
(5x4) × (x2)3 × (2x)2
Find the value of (5x6) × (−1.5x2y3) × (−12xy2) when x = 1, y = 0.5.
Find the following product:
0.1y(0.1x5 + 0.1y)
Find the following product: \[- \frac{8}{27}xyz\left( \frac{3}{2}xy z^2 - \frac{9}{4}x y^2 z^3 \right)\]
Find the product −3y(xy + y2) and find its value for x = 4 and y = 5.
Multiply:
(5x + 3) by (7x + 2)
