Question Details

What is the value of (3x3 + 5x2y + 12xy2 + 7y3), when x = – 4 and y = – 1?

Options

A

– 329

B

– 359

C

– 361

D

– 327

Show Answer

Correct Answer :

Option D

– 327

– 327

Solution :

The correct answer is – 327.

We need to evaluate the expression 3x3+5x2y+12xy2+7y3 at x=-4 and y=-1.

Let us first compute each power we will need:

x2=(-4)2=16
x3=(-4)3=-64
y2=(-1)2=1
y3=(-1)3=-1

Now substitute into each term one by one:

Term 1: 3x3=3×(-64)=-192

Term 2: 5x2y=5×16×(-1)=80×(-1)=-80

Term 3: 12xy2=12×(-4)×1=-48

Term 4: 7y3=7×(-1)=-7

Now add all four terms together:

(-192)+(-80)+(-48)+(-7)
=-192-80-48-7
=-327

Therefore, the value of 3x3+5x2y+12xy2+7y3 when x=-4 and y=-1 is – 327.

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