Question Details

If A = x2 (1 − 3y2), B = x (xy2 − 2x) and C = 3y (y − 4x2y), then A + B − C = px2 + qx2y2 + ry2.
What is the value of (5p + q − r) ?

Options

A

12

B

10

C

18

D

8

Show Answer

Correct Answer :

Option D

8

Solution :

The correct answer is 8.

Given the expressions:

A=x2(13y2)

B=x(xy22x)

C=3y(y4x2y)

First, expand each of the given algebraic expressions:

A=x23x2y2

B=x2y22x2

C=3y212x2y2

Now, calculate A+BC:

A+BC=(x23x2y2)+(x2y22x2)(3y212x2y2)

Group the like terms together:

A+BC=(x22x2)+(3x2y2+x2y2+12x2y2)3y2

A+BC=x2+10x2y23y2

Comparing this result with the given form px2+qx2y2+ry2:

p=1
q=10
r=3

Now evaluate 5p+qr:

5p+qr=5(1)+10(3)

5p+qr=5+10+3=8

Thus, the value of 5p+qr is 8.

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