Question

Find the coefficient of x in the expansion of (1-3x+7x^2)(1-x)^16

Answer 1

Answer:

Step-by-step explanation:

1−3x+7x2)(1−x)16(1−3x+7x2)(1−x)16

⇒(1−3x+7x2)[16C0x0−16C1x+16C2x2......+16Cn−1(−1)n−1xn−1+nCn(−1)6nxn]⇒(1−3x+7x2)[16C0x0−16C1x+16C2x2......+16Cn−1(−1)n−1xn−1+nCn(−1)6nxn]

⇒(1−3x+7x2)[1−16C1x+16C2x2+16C3x3+16C4x4+16C5x5+......16C16x16]⇒(1−3x+7x2)[1−16C1x+16C2x2+16C3x3+16C4x4+16C5x5+......16C16x16]

⇒−3.16C1⇒−3.16C1

⇒−3×16!1!15!⇒−3×16!1!15!

⇒−3×16⇒−3×16

⇒−48