Advertisements
Advertisements
प्रश्न
Simplify:
(3x + 2y)(4x + 3y) − (2x − y)(7x − 3y)
Advertisements
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:
\[\left( 0 . 5x \right) \times \left( \frac{1}{3}x y^2 z^4 \right) \times \left( 24 x^2 yz \right)\]
Find the following product:
−5a(7a − 2b)
Find the following product:
0.1y(0.1x5 + 0.1y)
Multiply:
[−3d + (−7f)] by (5d + f)
Multiply:
(0.8a − 0.5b) by (1.5a − 3b)
Simplify:
x2(x − y) y2(x + 2y)
Simplify:
(2x2 + 3x − 5)(3x2 − 5x + 4)
Simplify:
(3x − 2)(2x − 3) + (5x − 3)(x + 1)
Simplify : (m2 − n2m)2 + 2m3n2
