find the the coefficient of x4 in the expansion of (1+ x -2x2)7 - Maths - Binomial Theorem

Question

find the the coefficient of x4 in the expansion of (1+ x
-2x2)7

Priyanka Kedia · Accepted Answer

1+x-2x27=1-x1+2x7=1-x71+2x7=1-C17x+C27x2-C37x3+C47x4-
×1+C172x+C272x2+C372x3+C472x4+
Multiply and then the term of x4 will be,1×C4724-C17C3723+C27C2722-C37C172+C471x4=35×16-7×35×8+21×21×4-35×7×2+35×1x4=560-1960+1764-490+35x4=-91x4Hence, the coefficient of x is -91

find the the coefficient of x4 in the expansion of (1+ x -2x2)7.

find the the coefficient of x⁴ in the expansion of (1+ x -2x²)^7.