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CTET Paper II (Mathematics and Science) 22 Dec 2021 Solved Paper

Question : 39 of 150

Marks: +1, -0

Let

p = 2x^{4} - x^{3}y^{3} + 7y^{4},

q = x4 + 3x3y3 - 5y4

r = 3x4 - 4x3y3 + 2y4

Then, p + q - r is equal to

Solution:

Concept:

Add and subtract polynomials by combining like terms after removing brackets.

Explanation:

Write the expression:

(2x^4 - x^3y^3 + 7y^4) + (x^4 + 3x^3y^3 - 5y^4) - (3x^4 - 4x^3y^3 + 2y^4)

Remove brackets carefully:

2x^4 - x^3y^3 + 7y^4 + x^4 + 3x^3y^3 - 5y^4 - 3x^4 + 4x^3y^3 - 2y^4

Combine

x^4

terms:

2x^4 + x^4 - 3x^4 = 0

Combine

x^3y^3

terms:

-x^3y^3 + 3x^3y^3 + 4x^3y^3 = 6x^3y^3

Combine

y^4

terms:

7y^4 - 5y^4 - 2y^4 = 0

The simplified result is

6x^3y^3

Answer:

6x^3y^3

(Option D)

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