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प्रश्न
Simplify:
(2x2 + 3x − 5)(3x2 − 5x + 4)
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उत्तर
To simplify, we will proceed as follows:
\[\left( 2 x^2 + 3x - 5 \right)\left( 3 x^2 - 5x + 4 \right)\]
\[= 2 x^2 \left( 3 x^2 - 5x + 4 \right) + 3x\left( 3 x^2 - 5x + 4 \right) - 5\left( 3 x^2 - 5x + 4 \right)\] (Distributive law)
\[= 6 x^4 - 10 x^3 + 8 x^2 + 9 x^3 - 15 x^2 + 12x - 15 x^2 + 25x - 20\]
\[= 6 x^4 - 10 x^3 + 9 x^3 + 8 x^2 - 15 x^2 - 15 x^2 + 12x + 25x - 20\] (Rearranging)
\[= 6 x^4 - x^3 - 22 x^2 + 36x - 20\] (Combining like terms)
Thus, the answer is \[6 x^4 - x^3 - 22 x^2 + 36x - 20\].
संबंधित प्रश्न
Find each of the following product:
(−5a) × (−10a2) × (−2a3)
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.
\[\left( \frac{3}{5} x^2 y \right) \times \left( - \frac{15}{4}x y^2 \right) \times \left( \frac{7}{9} x^2 y^2 \right)\]
Simplify: 2x2(x3 − x) − 3x(x4 + 2x) − 2(x4 − 3x2)
Simplify: x2(x2 + 1) − x3(x + 1) − x(x3 − x)
Multiply:
(3x2 + y2) by (2x2 + 3y2)
Multiply:
(2x2 − 1) by (4x3 + 5x2)
Simplify:
(x2 − 2y2) (x + 4y) x2y2
Multiply:
23xy2 × 4yz2
