Factorise : 1 + 64x³
Solution:
Given, the expression is 1 + 64x³
We have to factorise the given expression.
Using the algebraic identity,
a³ + b³ = (a + b)(a² + b² - ab)
1 + 64x³ = (1)³ - (4x)³
Here a = 1 and b = 4x
(1)³ + (4x)³ = (1 + 4x)((1)² + (4x)² - (1)(4x))
= (1 + 4x)(1 + 16x² - 4x)
Therefore, the factors are (1 + 4x)(1 + 16x² - 4x)
✦ Try This: Factorise : 1 + 8x³
Given, the expression is 1 + 8x³
We have to factorise the given expression.
Using the algebraic identity,
a³ + b³ = (a + b)(a² + b² - ab)
1 + 8x³ = (1)³ - (2x)³
Here a = 1 and b = 2x
(1)³ + (2x)³ = (1 + 2x)((1)² + (2x)² - (1)(2x))
= (1 + 2x)(1 + 4x² - 2x)
Therefore, the factors are (1 + 2x)(1 + 4x² - 2x)
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 2
NCERT Exemplar Class 9 Maths Exercise 2.3 Problem 34(i)
Factorise : 1 + 64x³
Summary:
On factorising 1 + 64x³ using the algebraic identity we get (1 + 4x)(1 + 16x² - 4x)
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