Find the following products : (x/2 + 2y)(x²/4 - xy + 4y²)
Solution:
Given, the expression is (x/2 + 2y)(x²/4 - xy + 4y²)
We have to find the product of the expression.
(x/2 + 2y)(x²/4 - xy + 4y²) = x/2(x²/4 - xy + 4y²) + 2y(x²/4 - xy + 4y²)
By multiplicative and distributive property,
x/2(x²/4 - xy + 4y²) = x/2(x²/4) - x/2(xy) + x/2(4y²)
= x³/8 - x²y/2 + 4xy²/2
= x³/8 - x²y/2 + 2xy²
By multiplicative and distributive property,
2y(x²/4 - xy + 4y²) = 2y(x²/4) - 2y(xy) + 2y(4y²)
= 2x²y/4 - 2xy² + 8y³
= x²y/2 - 2xy² + 8y³
So, (x/2 + 2y)(x²/4 - xy + 4y²) = x³/8 - x²y/2 + 2xy² + x²y/2 - 2xy² + 8y³
By grouping,
= x³/8 + x²y/2 - x²y/2 - 2xy² + 2xy² + 8y³
= x³/8 + 8y³
Therefore, the product of the expression is x³/8 + 8y³.
✦ Try This: Find the following products : (x²/4 - 1/3) (x⁴/2 + x² + 5/11)
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 2
NCERT Exemplar Class 9 Maths Exercise 2.3 Problem 33(i)
Find the following products : (x/2 + 2y)(x²/4 - xy + 4y²)
Summary:
The product of (x/2 + 2y)(x²/4 - xy + 4y²) using the multiplicative and distributive property is x³/8 + 8y³
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