Advertisements
Advertisements
Question
Simplify:
(3x + 2y)(4x + 3y) − (2x − y)(7x − 3y)
Advertisements
Solution
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
RELATED QUESTIONS
Find each of the following product:
(−5a) × (−10a2) × (−2a3)
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:
−11a(3a + 2b)
Find the following product: \[\left( - \frac{7}{4}a b^2 c - \frac{6}{25} a^2 c^2 \right)( - 50 a^2 b^2 c^2 )\]
Find the following product: \[- \frac{8}{27}xyz\left( \frac{3}{2}xy z^2 - \frac{9}{4}x y^2 z^3 \right)\]
Multiply:
(3x2 + y2) by (2x2 + 3y2)
Multiply:
(x6 − y6) by (x2 + y2)
Multiply:
[−3d + (−7f)] by (5d + f)
Multiply: \[\left( - \frac{a}{7} + \frac{a^2}{9} \right)by\left( \frac{b}{2} - \frac{b^2}{3} \right)\].
Simplify : (m2 − n2m)2 + 2m3n2
