the coefficient of w² in the expansion of (w-2)³ is
Answers
Answered by
0
Step-by-step explanation:
We know that the formula for (a+b)
3
is:
(a+b)
3
=a
3
+b
3
+3a
2
b+3ab
2
Now, let us substitute a=x and b=2 in the above formula as shown below:
(x+2)
3
=x
3
+2
3
+(3x
2
×2)+(3x×2
2
)
=x
3
+8+6x
2
+(3x×4)
=x
3
+8+6x
2
+12x
=x
3
+6x
2
+12x+8
From the above calculations, we observe that the coefficient of x
3
is 1, coefficient of x
2
is 6 and coefficient of x is 12.
Hence, the coefficient of x is 12.
Answered by
1
Answer:
(a-b) ³ = a³-b³-3a²b+3ab²
(w-2)³ = w³-2³-3*w²*2+3w*4
(w-2)³ = w³-8-6w²+12w
hence coefficient of x² is -6
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