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Question

# Let P(x)=4x2+9y2+16z2+12xy+24yz+16xz factorize P(x) for x=1,y=1,z=1.

A
36
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B
49
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C
64
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D
81
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Solution

## The correct option is A 81We know that one of the formula is (a+b+c)2=a2+b2+c2+2ab+2bc+2ca.In the given polynomial 4x2+9y2+16z2+12xy+24yz+16xz, we observe that a=2x,b=3y and c=4z, therefore, comparing with the above formula, we get:4x2+9y2+16z2+12xy+24yz+16xz=(2x)2+(3y)2+(4z)2+(2×2x×3y)+(2×3y×4z)+(2×4z×2x) =(2x+3y+4z)2Let us substitute x=1,y=1 and z=1 in (2x+3y+4z)2 as shown below:[(2×1)+(3×1)+(4×1)]2=(2+3+4)2=92=81Hence, 4x2+9y2+16z2+12xy+24yz+16xz=81 if x=1,y=1 and z=1.

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