Advertisements
Advertisements
Question
Simplify:
(5 − x)(6 − 5x)( 2 − x)
Advertisements
Solution
To simplify, we will proceed as follows:
\[\left( 5 - x \right)\left( 6 - 5x \right)\left( 2 - x \right)\]
\[ = \left[ \left( 5 - x \right)\left( 6 - 5x \right) \right]\left( 2 - x \right)\]
\[= \left[ 5\left( 6 - 5x \right) - x\left( 6 - 5x \right) \right]\left( 2 - x \right)\] (Distributive law)
\[= \left( 30 - 25x - 6x + 5 x^2 \right)\left( 2 - x \right)\]
\[ = \left( 30 - 31x + 5 x^2 \right)\left( 2 - x \right)\]
\[ = 2\left( 30 - 31x + 5 x^2 \right) - x\left( 30 - 31x + 5 x^2 \right)\]
\[ = 60 - 62x + 10 x^2 - 30x + 31 x^2 - 5 x^3\]
\[= 60 - 62x - 30x + 10 x^2 + 31 x^2 - 5 x^3\] (Rearranging)
\[= 60 - 92x + 41 x^2 - 5 x^3\] (Combining like terms)
Thus, the answer is \[60 - 92x + 41 x^2 - 5 x^3\].
APPEARS IN
RELATED QUESTIONS
Find each of the following product:
\[\left( - \frac{1}{27} a^2 b^2 \right) \times \left( \frac{9}{2} a^3 b^2 c^2 \right)\]
Express each of the following product as a monomials and verify the result in each case for x = 1:
(3x) × (4x) × (−5x)
Express each of the following product as a monomials and verify the result in each case for x = 1:
(5x4) × (x2)3 × (2x)2
Find the following product:
−11a(3a + 2b)
Find the following product: \[\frac{4}{3}a( a^2 + b^2 - 3 c^2 )\]
Find the product −3y(xy + y2) and find its value for x = 4 and y = 5.
Multiply:
(x6 − y6) by (x2 + y2)
Multiply:
(2x2y2 − 5xy2) by (x2 − y2)
Simplify:
(x2 − 2y2) (x + 4y) x2y2
Simplify:
(5x − 3)(x + 2) − (2x + 5)(4x − 3)
