Find the following products : (x² - 1) (x⁴ + x² + 1)
Solution:
Given, the expression is (x² - 1) (x⁴ + x² + 1)
We have to find the product of the expression.
(x² - 1) (x⁴ + x² + 1) = x²(x⁴ + x² + 1) - 1(x⁴ + x² + 1)
By multiplicative and distributive property,
x²(x⁴ + x² + 1) = x²(x⁴) + x²(x²) + x²(1)
= x⁶ + x⁴ + x²
By multiplicative and distributive property,
1(x⁴ + x² + 1) = x⁴ + x² + 1
So, x²(x⁴ + x² + 1) - 1(x⁴ + x² + 1) = x⁶ + x⁴ + x² - (x⁴ + x² + 1)
= x⁶ + x⁴ + x² - x⁴ - x² - 1
By grouping,
= x⁶ + x⁴ - x⁴ + x² - x² - 1
= x⁶ - 1
Therefore, the product of the expression is x⁶ - 1
✦ Try This: Find the following products : (x + 1) (x³ + x² + 1)
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 2
NCERT Exemplar Class 9 Maths Exercise 2.3 Problem 33(ii)
Find the following products : (x² - 1) (x⁴ + x² + 1)
Summary:
The product of (x² - 1) (x⁴ + x² + 1) using the multiplicative and distributive property is x⁶ - 1
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