Advertisements
Advertisements
Question
Simplify:
(5x − 3)(x + 2) − (2x + 5)(4x − 3)
Advertisements
Solution
To simplify, we will proceed as follows:
\[\left( 5x - 3 \right)\left( x + 2 \right) - \left( 2x + 5 \right)\left( 4x - 3 \right)\]
\[ = \left[ \left( 5x - 3 \right)\left( x + 2 \right) \right] - \left[ \left( 2x + 5 \right)\left( 4x - 3 \right) \right]\]
\[= \left[ 5x\left( x + 2 \right) - 3\left( x + 2 \right) \right] - \left[ 2x\left( 4x - 3 \right) + 5\left( 4x - 3 \right) \right]\] (Distributive law)
\[= 5 x^2 + 10x - 3x - 6 - 8 x^2 + 6x - 20x + 15\]
\[= 5 x^2 - 8 x^2 + 10x - 3x + 6x - 20x - 6 + 15\] (Rearranging)
\[= 5 x^2 - 8 x^2 + 10x - 3x + 6x - 20x - 6 + 15\]
\[ = - 3 x^2 - 7x + 9\] (Combining like terms)
Hence, the answer is \[- 3 x^2 - 7x + 9\].
APPEARS IN
RELATED QUESTIONS
Find each of the following product:
(−5xy) × (−3x2yz)
Find each of the following product:
\[\left( - \frac{2}{7} a^4 \right) \times \left( - \frac{3}{4} a^2 b \right) \times \left( - \frac{14}{5} b^2 \right)\]
Find each of the following product: \[\left( \frac{4}{3}p q^2 \right) \times \left( - \frac{1}{4} p^2 r \right) \times \left( 16 p^2 q^2 r^2 \right)\]
Evaluate (3.2x6y3) × (2.1x2y2) when x = 1 and y = 0.5.
Find the following product: \[\frac{6x}{5}( x^3 + y^3 )\]
Find the product 24x2 (1 − 2x) and evaluate its value for x = 3.
Simplify: a(b − c) − b(c − a) − c(a − b)
Simplify: a2b(a3 − a + 1) − ab(a4 − 2a2 + 2a) − b (a3 − a2 − 1)
Find the following product and verify the result for x = − 1, y = − 2: \[\left( \frac{1}{3}x - \frac{y^2}{5} \right)\left( \frac{1}{3}x + \frac{y^2}{5} \right)\]
What is the product of 3x and 4x²?
