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प्रश्न
Simplify:
x2(x − y) y2(x + 2y)
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उत्तर
To simplify, we will proceed as follows:
\[x^2 \left( x - y \right) y^2 \left( x + 2y \right)\]
\[ = \left[ x^2 \left( x - y \right) \right]\left[ y^2 \left( x + 2y \right) \right]\]
\[ = \left( x^3 - x^2 y \right)\left( x y^2 + 2 y^3 \right)\]
\[ = x^3 \left( x y^2 + 2 y^3 \right) - x^2 y\left( x y^2 + 2 y^3 \right)\]
\[ = x^4 y^2 + 2 x^3 y^3 - \left[ x^3 y^3 + 2 x^2 y^4 \right]\]
\[ = x^4 y^2 + 2 x^3 y^3 - x^3 y^3 - 2 x^2 y^4 \]
\[ = x^4 y^2 + x^3 y^3 - 2 x^2 y^4\]
Thus, the answer is \[x^4 y^2 + x^3 y^3 - 2 x^2 y^4\].
संबंधित प्रश्न
Express each of the following product as a monomials and verify the result in each case for x = 1:
(4x2) × (−3x) × \[\left( \frac{4}{5} x^3 \right)\]
Evaluate each of the following when x = 2, y = −1.
\[(2xy) \times \left( \frac{x^2 y}{4} \right) \times \left( x^2 \right) \times \left( y^2 \right)\]
Find the following product:
250.5xy \[\left( xz + \frac{y}{10} \right)\]
Multiply:
(a − 1) by (0.1a2 + 3)
Multiply:
(3x2 + y2) by (2x2 + 3y2)
Multiply: \[\left( \frac{3}{5}x + \frac{1}{2}y \right) by \left( \frac{5}{6}x + 4y \right)\]
Find the following product and verify the result for x = − 1, y = − 2:
(3x − 5y) (x + y)
Simplify:
(2x2 + 3x − 5)(3x2 − 5x + 4)
Simplify : (4m − 8n)2 + (7m + 8n)2
Show that: (4pq + 3q)2 − (4pq − 3q)2 = 48pq2
