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 \[- 2 x^2 + 30xy + 3 y^2\].
APPEARS IN
संबंधित प्रश्न
Find each of the following product: \[\left( \frac{- 24}{25} x^3 z \right) \times \left( - \frac{15}{16}x z^2 y \right)\]
Find each of the following product:
\[\left( - \frac{1}{27} a^2 b^2 \right) \times \left( \frac{9}{2} a^3 b^2 c^2 \right)\]
Find each of the following product: \[\left( \frac{4}{3} u^2 vw \right) \times \left( - 5uv w^2 \right) \times \left( \frac{1}{3} v^2 wu \right)\]
Evaluate (3.2x6y3) × (2.1x2y2) when x = 1 and y = 0.5.
Evaluate (−8x2y6) × (−20xy) for x = 2.5 and y = 1.
Multiply:
(2x2y2 − 5xy2) by (x2 − y2)
Simplify:
(2x2 + 3x − 5)(3x2 − 5x + 4)
Simplify : (2.5p − 1.5q)2 − (1.5p − 2.5q)2
Show that: (4pq + 3q)2 − (4pq − 3q)2 = 48pq2
What is the product of 3x and 4x²?
