If P = 3x² + y², Q = 2x² + 3y² and R = 4x^{4} + 5y^{4}} then, P × Q - R is equal to

Correct Answer is : 2x4+11x2y2−2y42x^{4} + 11x²y² - 2y^{4}2x4+11x2y2−2y4

If P = 3x² + y², Q = 2x² + 3y² and R = 4x^{4} + 5y^{4}} then, P × Q - R is equal to

Correct Answer is : 2x4+11x2y2−2y42x^{4} + 11x²y² - 2y^{4}2x4+11x2y2−2y4

Test Index

CTET Paper II (Mathematics and Science) 6 Jan 2022 Solved Paper

Question : 40 of 150

Marks: +1, -0

If P = 3x^{2} + y^{2},

Q = 2x^{2} + 3y^{2}

and

R = 4x^{4} + 5y^{4}

}

then, P × Q - R is equal to

$2x^{4} + 11x^{2}y^{2} - 2y^{4}$
$2x^{4} + 9x^{2}y^{2} - 2y^{4}$
$2x^{4} + 13x^{2}y^{2} + 2y^{4}$
$2x^{4} + 10x^{2}y^{2} + 2y^{4}$

Validate

Solution:

Concept:

To simplify the expression, multiply the polynomials P and Q, then subtract R. Use the distributive property (FOIL method) for multiplication and combine like terms.

Explanation:

First, multiply P by Q:

(3x^2 + y^2) \times (2x^2 + 3y^2)

= 3x^2 \cdot 2x^2 + 3x^2 \cdot 3y^2 + y^2 \cdot 2x^2 + y^2 \cdot 3y^2

= 6x^4 + 9x^2y^2 + 2x^2y^2 + 3y^4

= 6x^4 + 11x^2y^2 + 3y^4

Now subtract R from this result:

P \times Q - R = (6x^4 + 11x^2y^2 + 3y^4) - (4x^4 + 5y^4)

Combine like terms:

x^4

terms:

6x^4 - 4x^4 = 2x^4

x^2y^2

term:

11x^2y^2

(unchanged)

y^4

terms:

3y^4 - 5y^4 = -2y^4

So the result is

2x^4 + 11x^2y^2 - 2y^4

Answer:

2x^{4} + 11x^{2}y^{2} - 2y^{4}

Go to Question:

Prev Question

Next Question