Question
Simplify:
$(2 x-1)(2 x+1)\left(4 x^2+1\right)\left(16 x^4+1\right)$
$(2 x-1)(2 x+1)\left(4 x^2+1\right)\left(16 x^4+1\right)$
✓
Answer
To simplify, we will proceed as follows:
To simplify, we will proceed as follows:
$(2 x-1)(2 x+1)\left(4 x^2+1\right)\left(16 x^4+1\right)$
$=\left((2 x)^2-1^2\right)\left(4 x^2+1\right)\left(16 x^4+1\right)\left[\because(a+b)(a-b)=a^2-b^2\right]$
$=\left(4 x^2-1\right)\left(4 x^2+1\right)\left(16 x^4+1\right)$
$=\left\{\left(4 x^2\right)^2-\left(1^2\right)^2\right\}\left(16 x^4+1\right)\left[\because(a+b)(a-b)=a^2-b^2\right]$
$=\left(16 x^4-1\right)\left(16 x^4+1\right)$
$=\left(16 x^4\right)^2-1^2\left[\because(a+b)(a-b)=a^2-b^2\right]$
$=256 x^8-1$
To simplify, we will proceed as follows:
$(2 x-1)(2 x+1)\left(4 x^2+1\right)\left(16 x^4+1\right)$
$=\left((2 x)^2-1^2\right)\left(4 x^2+1\right)\left(16 x^4+1\right)\left[\because(a+b)(a-b)=a^2-b^2\right]$
$=\left(4 x^2-1\right)\left(4 x^2+1\right)\left(16 x^4+1\right)$
$=\left\{\left(4 x^2\right)^2-\left(1^2\right)^2\right\}\left(16 x^4+1\right)\left[\because(a+b)(a-b)=a^2-b^2\right]$
$=\left(16 x^4-1\right)\left(16 x^4+1\right)$
$=\left(16 x^4\right)^2-1^2\left[\because(a+b)(a-b)=a^2-b^2\right]$
$=256 x^8-1$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
A wooden cylindrical pole is 7m high and its base radius is 10cm. Find its weight if the wood weighs 225kg per cubic metre.
Factorize :
20x² – 26x + 8
Simplify :
(3k – 4r – 2m)² – (3k + 4r – 2m)²
The diameters PQ and RS of the circle with centre C are perpendicular to each other at C. State, why arc PS and arc SQ are congruent. Write the other arcs which are congruent to arc PS.
Find the volume, lateral surface area and the total surface area of the cuboid whose dimensions are:
Length = 24m, breadth = 25cm and height = 6m
Length = 24m, breadth = 25cm and height = 6m
Find three rational numbers between 4 and 5.
The area of a trapezium is $180 cm^2$ and its height is 9 cm . If one of the parallel sides is longer than the other by 6 cm , find the two parallel sides.
→Find the volume, lateral surface area and the total surface area of the cuboid whose dimensions are:
Length $=48 cm$, breadth $=6 dm$ and height $=1 m$.
→Length $=48 cm$, breadth $=6 dm$ and height $=1 m$.
A shopkeeper alllows his custmers 10% off on the marked price of goods and still gets a profit of 25%. What is the actual cost to him of an article marked Rs. 250?
Sonu buys 40kg of wheat at Rs. 12.50/kg and 30kg of wheat at Rs. 14/kg. At what rate /kg should he sell the mixture to gain 5% on the whole?