Find the following product : (2x - y + 3z) (4x² + y² + 9z² + 2xy + 3yz - 6xz)
Solution:
Given, the expression is (2x - y + 3z) (4x² + y² + 9z² + 2xy + 3yz - 6xz)
We have to find the product of the expression.
(2x - y + 3z) (4x² + y² + 9z² + 2xy + 3yz - 6xz) = 2x(4x² + y² + 9z² + 2xy + 3yz - 6xz) - y(4x² + y² + 9z² + 2xy + 3yz - 6xz) + 3z(4x² + y² + 9z² + 2xy + 3yz - 6xz)
By multiplicative and distributive property,
2x(4x² + y² + 9z² + 2xy + 3yz - 6xz) = 2x(4x²) + 2x(y²) + 2x(9z²) + 2x(2xy) + 2x(3yz) - 2x(6xz)
= 8x³ + 2xy² + 18xz² + 4x²y + 6xyz - 12x²z
By multiplicative and distributive property,
y(4x² + y² + 9z² + 2xy + 3yz - 6xz) = y(4x²) + y(y²) + y(9z²) + y(2xy) + y(3yz) - y(6xz)
= 4x²y + y³ + 9yz² + 2xy² + 3y²z - 6xyz
By multiplicative and distributive property,
3z(4x² + y² + 9z² + 2xy + 3yz - 6xz) = 3z(4x²) + 3z(y²) + 3z(9z²) + 3z(2xy) + 3z(3yz) - 3z(6xz)
= 12x²z + 3y²z + 27z³ + 6xyz + 9yz² - 18xz²
Now, (2x - y + 3z) (4x² + y² + 9z² + 2xy + 3yz - 6xz) = 8x³ + 2xy² + 18xz² + 4x²y + 6xyz - 12x²z - (4x²y + y³ + 9yz² + 2xy² + 3y²z - 6xyz) + 12x²z + 3y²z + 27z³ + 6xyz + 9yz² - 18xz²
= 8x³ + 2xy² + 18xz² + 4x²y + 6xyz - 12x²z - 4x²y - y³ - 9yz² - 2xy² - 3y²z + 6xyz + 12x²z + 3y²z + 27z³ + 6xyz + 9yz² - 18xz²
By grouping,
= 8x³ - y³ + 27z³ + 4x²y - 4x²y + 2xy² - 2xy² + 18xz² - 18xz² + 6xyz + 6xyz + 6xyz - 9yz² + 9yz² - 12x²z + 12x²z + 3y²z - 3y²z
= 8x³ - y³ + 27z³ + 18xyz
Therefore, the product is 8x³ - y³ + 27z³ + 18xyz
✦ Try This: Find the following product : (2x - 2y - 3z) (x² + y² + z² + xy + 3yz + xz)
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 2
NCERT Exemplar Class 9 Maths Exercise 2.3 Problem 35
Find the following product : (2x - y + 3z) (4x² + y² + 9z² + 2xy + 3yz - 6xz)
Summary:
The product of (2x - y + 3z) (4x² + y² + 9z² + 2xy + 3yz - 6xz) is 8x³ - y³ + 27z³ + 18xyz
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