Subtract the sum of - 3x³y² + 2x²y³ and - 3x²y³ - 5y⁴ from x⁴ + x³y² + x²y³ + y⁴.
Solution:
Given, the expressions are - 3x³y² + 2x²y³, - 3x²y³ - 5y⁴ and x⁴ + x³y² + x²y³ + y⁴.
We have to subtract the sum of - 3x³y² + 2x²y³ and - 3x²y³ - 5y⁴ from x⁴ + x³y² + x²y³ + y⁴.
Sum of - 3x³y² + 2x²y³ and - 3x²y³ - 5y⁴ = - 3x³y² + 2x²y³ + (- 3x²y³ - 5y⁴)
= -3x³y² + 2x²y³ - 3x²y³ - 5y⁴
= -3x³y² + (2 - 3) x²y³ - 5y⁴
= -3x³y² + (-1) x²y³ - 5y⁴
= -3x³y² - x²y³ - 5y⁴
Now, subtract -3x³y² - x²y³ - 5y⁴ from x⁴ + x³y² + x²y³ + y⁴,
= (x⁴ + x³y² + x²y³ + y⁴) - (-3x³y² - x²y³ - 5y⁴)
By distributive property,
= x⁴ + x³y² + x²y³ + y⁴ -(-3x³y²) - (-x²y³) - (-5y⁴)
= x⁴ + x³y² + x²y³ + y⁴ + 3x³y² + x²y³ + 5y⁴
By grouping like terms,
= x⁴ + x³y² + 3x³y² + x²y³ + x²y³ + y⁴ + 5y⁴
= x⁴ + (1 + 3)x³y² + (1 + 1)x²y³ + (1 + 5)y⁴
= x⁴ + 4x³y² + 2x²y³ + 6y⁴
Therefore, the required expression is x⁴ + 4x³y² + 2x²y³ + 6y⁴.
✦ Try This: Subtract the sum of 4x³y² + 3x²y³ and 5x²y³ - 3y⁴ from 4x⁴ + 3x³y² + 2x²y³ - y⁴.
☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 12
NCERT Exemplar Class 7 Maths Chapter 10 Sample Problem 14
Subtract the sum of - 3x³y² + 2x²y³ and - 3x²y³ - 5y⁴ from x⁴ + x³y² + x²y³ + y⁴.
Summary:
On subtracting the sum of - 3x³y² + 2x²y³ and - 3x²y³ - 5y⁴ from x⁴ + x³y² + x²y³ + y⁴, we get x⁴ + 4x³y² + 2x²y³ + 6y⁴.
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