Advertisements
Advertisements
प्रश्न
Simplify : (2x − 1)(2x + 1)(4x2 + 1)(16x4 + 1)
Advertisements
उत्तर
To simplify, we will proceed as follows:
\[ \left( 2x - 1 \right)\left( 2x + 1 \right)\left( 4 x^2 + 1 \right)\left( 16 x^4 + 1 \right)\]
\[ = \left( \left( 2x \right)^2 - 1^2 \right)\left( 4 x^2 + 1 \right)\left( 16 x^4 + 1 \right) \left[ \because \left( a + b \right)\left( a - b \right) = a^2 - b^2 \right] \]
\[ = \left( 4 x^2 - 1 \right)\left( 4 x^2 + 1 \right)\left( 16 x^4 + 1 \right) \]
\[ = \left\{ \left( 4 x^2 \right)^2 - \left( 1^2 \right)^2 \right\}\left( 16 x^4 + 1 \right) \left[ \because \left( a + b \right)\left( a - b \right) = a^2 - b^2 \right]\]
\[ = \left( 16 x^4 - 1 \right) \left( 16 x^4 + 1 \right) \]
\[ = \left( 16 x^4 \right)^2 - 1^2 \left[ \because \left( a + b \right)\left( a - b \right) = a^2 - b^2 \right]\]
\[ = 256 x^8 - 1\]
APPEARS IN
संबंधित प्रश्न
Find each of the following product: \[( - 7xy) \times \left( \frac{1}{4} x^2 yz \right)\]
Express each of the following product as a monomials and verify the result in each case for x = 1:
(x2)3 × (2x) × (−4x) × (5)
Write down the product of −8x2y6 and −20xy. Verify the product for x = 2.5, y = 1.
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: \[\frac{4}{3}a( a^2 + b^2 - 3 c^2 )\]
Multiply:
(2x2y2 − 5xy2) by (x2 − y2)
Find the following product and verify the result for x = − 1, y = − 2:
(3x − 5y) (x + y)
Simplify:
(x2 − 3x + 2)(5x − 2) − (3x2 + 4x − 5)(2x − 1)
Multiply:
(12a + 17b) × 4c
