Advertisements
Advertisements
Question
Simplify:
(x2 − 3x + 2)(5x − 2) − (3x2 + 4x − 5)(2x − 1)
Solution
To simplify, we will proceed as follows:
\[\left( x^2 - 3x + 2 \right)\left( 5x - 2 \right) - \left( 3 x^2 + 4x - 5 \right)\left( 2x - 1 \right)\]
\[ = \left[ \left( x^2 - 3x + 2 \right)\left( 5x - 2 \right) \right] - \left[ \left( 3 x^2 + 4x - 5 \right)\left( 2x - 1 \right) \right]\]
\[= \left[ 5x\left( x^2 - 3x + 2 \right) - 2\left( x^2 - 3x + 2 \right) \right] - \left[ 2x\left( 3 x^2 + 4x - 5 \right) - 1 \times \left( 3 x^2 + 4x - 5 \right) \right]\] (Distributive law)
\[= \left[ 5 x^3 - 15 x^2 + 10x - \left( 2 x^2 - 6x + 4 \right) \right] - \left[ 6 x^3 + 8 x^2 - 10x - 3 x^2 - 4x + 5 \right]\]
\[ = \left[ 5 x^3 - 15 x^2 + 10x - 2 x^2 + 6x - 4 \right] - \left[ 6 x^3 + 8 x^2 - 10x - 3 x^2 - 4x + 5 \right]\]
\[ = 5 x^3 - 15 x^2 + 10x - 2 x^2 + 6x - 4 - 6 x^3 - 8 x^2 + 10x + 3 x^2 + 4x - 5\]
\[= 5 x^3 - 6 x^3 - 15 x^2 - 2 x^2 - 8 x^2 + 3 x^2 + 10x + 6x + 10x + 4x - 5 - 4\] (Rearranging)
\[= - x^3 - 22 x^2 + 30x - 9\] (Combining like terms)
Thus, the answer is \[- x^3 - 22 x^2 + 30x - 9\].
APPEARS IN
RELATED QUESTIONS
Express each of the following product as a monomials and verify the result in each case for x = 1:
(5x4) × (x2)3 × (2x)2
Simplify: a(b − c) − b(c − a) − c(a − b)
Simplify: a2b(a3 − a + 1) − ab(a4 − 2a2 + 2a) − b (a3 − a2 − 1)
Multiply:
(2x + 8) by (x − 3)
Multiply:
(x2 + y2) by (3a + 2b)
Multiply:
[−3d + (−7f)] by (5d + f)
Simplify:
(5x − 3)(x + 2) − (2x + 5)(4x − 3)
Simplify:
(3x + 2y)(4x + 3y) − (2x − y)(7x − 3y)
Simplify : (4m − 8n)2 + (7m + 8n)2
Show that: \[\left( \frac{4m}{3} - \frac{3n}{4} \right)^2 + 2mn = \frac{16 m^2}{9} + \frac{9 n^2}{16}\]
