Advertisements
Advertisements
प्रश्न
Simplify:
(x3 − 2x2 + 3x − 4) (x −1) − (2x − 3)(x2 − x + 1)
Advertisements
उत्तर
To simplify,we will proceed as follows:
\[\left( x^3 - 2 x^2 + 3x - 4 \right)\left( x - 1 \right) - \left( 2x - 3 \right)\left( x^2 - x + 1 \right)\]
\[ = \left[ \left( x^3 - 2 x^2 + 3x - 4 \right)\left( x - 1 \right) \right] - \left[ \left( 2x - 3 \right)\left( x^2 - x + 1 \right) \right]\]
\[= \left[ x\left( x^3 - 2 x^2 + 3x - 4 \right) - 1\left( x^3 - 2 x^2 + 3x - 4 \right) \right] - \left[ 2x\left( x^2 - x + 1 \right) - 3\left( x^2 - x + 1 \right) \right]\] (Distributive law)
\[= \left[ x\left( x^3 - 2 x^2 + 3x - 4 \right) - 1\left( x^3 - 2 x^2 + 3x - 4 \right) \right] - \left[ 2x\left( x^2 - x + 1 \right) - 3\left( x^2 - x + 1 \right) \right]\]
\[ = x^4 - 2 x^3 + 3 x^2 - 4x - x^3 + 2 x^2 - 3x + 4 - \left[ 2 x^3 - 2 x^2 + 2x - 3 x^2 + 3x - 3 \right]\]
\[ = x^4 - 2 x^3 + 3 x^2 - 4x - x^3 + 2 x^2 - 3x + 4 - 2 x^3 + 2 x^2 - 2x + 3 x^2 - 3x + 3\]
\[= x^4 - 2 x^3 - 2 x^3 - x^3 + 3 x^2 + 2 x^2 + 2 x^2 + 3 x^2 - 4x - 3x - 2x - 3x + 4 + 3\]
(Rearranging)
\[= x^4 - 5 x^3 + 10 x^2 - 12x + 7\] (Combining like terms)
Thus, the answer is \[x^4 - 5 x^3 + 10 x^2 - 12x + 7\].
APPEARS IN
संबंधित प्रश्न
Find each of the following product:
(−4x2) × (−6xy2) × (−3yz2)
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: \[\left( \frac{7}{9}a b^2 \right) \times \left( \frac{15}{7}a c^2 b \right) \times \left( - \frac{3}{5} a^2 c \right)\]
xy(x3 − y3)
Find the following product:
1.5x(10x2y − 100xy2)
Simplify: a(b − c) − b(c − a) − c(a − b)
Multiply:
(2x + 8) by (x − 3)
Simplify:
(5x + 3)(x − 1)(3x − 2)
Show that: (3x + 7)2 − 84x = (3x − 7)2
What is the product of 3x and 4x²?
