Advertisements
Advertisements
Question
Simplify : (2x − 1)(2x + 1)(4x2 + 1)(16x4 + 1)
Advertisements
Solution
To simplify, we will proceed as follows:
\[ \left( 2x - 1 \right)\left( 2x + 1 \right)\left( 4 x^2 + 1 \right)\left( 16 x^4 + 1 \right)\]
\[ = \left( \left( 2x \right)^2 - 1^2 \right)\left( 4 x^2 + 1 \right)\left( 16 x^4 + 1 \right) \left[ \because \left( a + b \right)\left( a - b \right) = a^2 - b^2 \right] \]
\[ = \left( 4 x^2 - 1 \right)\left( 4 x^2 + 1 \right)\left( 16 x^4 + 1 \right) \]
\[ = \left\{ \left( 4 x^2 \right)^2 - \left( 1^2 \right)^2 \right\}\left( 16 x^4 + 1 \right) \left[ \because \left( a + b \right)\left( a - b \right) = a^2 - b^2 \right]\]
\[ = \left( 16 x^4 - 1 \right) \left( 16 x^4 + 1 \right) \]
\[ = \left( 16 x^4 \right)^2 - 1^2 \left[ \because \left( a + b \right)\left( a - b \right) = a^2 - b^2 \right]\]
\[ = 256 x^8 - 1\]
RELATED QUESTIONS
Find the following product:
2a3(3a + 5b)
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:
4.1xy(1.1x − y)
Simplify:
a2b2(a + 2b)(3a + b)
Simplify:
(5 − x)(6 − 5x)( 2 − x)
Simplify : (4m − 8n)2 + (7m + 8n)2
Simplify : (2.5p − 1.5q)2 − (1.5p − 2.5q)2
Show that: \[\left( \frac{4m}{3} - \frac{3n}{4} \right)^2 + 2mn = \frac{16 m^2}{9} + \frac{9 n^2}{16}\]
Solve the following equation.
5(x + 1) = 74
