Simplify (2x - 5y)³ - (2x + 5y)³
Solution:
Given, (2x - 5y)³ - (2x + 5y)³
We have to simplify the given expression.
Using the algebraic identity,
(a + b)³ = a³ + b³ + 3ab(a + b)
Here a = 2x and b = 5y
(2x + 5y)³ = (2x)³ + (5y)³ + 3(2x)(5y)(2x + 5y)
= 8x³ + 125y³ + 30xy(2x + 5y)
(2x + 5y)³ = 8x³ + 125y³ + 60x²y + 150xy²
Using the algebraic identity,
(a - b)³ = a³ - b³ + 3a(-b)(a - b)
Here a = 2x and b = 5y
(2x - 5y)³ = (2x)³ - (5y)³ + 3(2x)(-5y)(2x - 5y)
= 8x³ - 125y³ - 30xy(2x - 5y)
(2x + 5y)³ = 8x³ - 125y³ - 60x²y + 150xy²
Now, (2x - 5y)³ - (2x + 5y)³ = 8x³ - 125y³ - 60x²y + 150xy² - (8x³ + 125y³ + 60x²y + 150xy²)
= 8x³ - 125y³ - 60x²y + 150xy² - 8x³ - 125y³ - 60x²y - 150xy²
= - 125y³ - 125y³ - 60x²y - 60x²y
= -250y³ - 120x²y
Therefore, (2x - 5y)³ - (2x + 5y)³ = -250y³ - 120x²y
✦ Try This: Simplify (3x - 7y)³ - (3x + 7y)³
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 2
NCERT Exemplar Class 9 Maths Exercise 2.4 Problem 5
Simplify (2x - 5y)³ - (2x + 5y)³
Summary:
On simplifying (2x - 5y)³ - (2x + 5y)³ using the algebraic identity (a - b)³ = a³ - b³ + 3a(-b)(a - b) we get -250y³ - 120x²y
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