The coefficient of x8 in the expression (2+x)2(3+x)3(4+x)4 must be

Question

The coefficient of x8 in the expression (2+x)2(3+x)3(4+x)4 must be (A) 26 (B) 27 (C) 28 (D) 29

Tardigrade Admin · Accepted Answer

The expression (2+x)2(3+x)3(4+x)4 =(x+2)(x+2)(x+3)(x+3)(x+3)(x+4)(x+4)(x+4)(x+4) = x 9+(2+2+3+3+3+4+4+4+4) x8+ ldots ldots ldots ldots. Co-efficient of x8=29

Q. The coefficient of $x^{8}$ in the expression $(2 + x)^{2} (3 + x)^{3} (4 + x)^{4}$ must be

26

27

28

29

The expression $(2 + x)^{2} (3 + x)^{3} (4 + x)^{4}$
$= (x + 2) (x + 2) (x + 3) (x + 3) (x + 3) (x + 4) (x + 4) (x + 4) (x + 4)$
$= x^{9} + (2 + 2 + 3 + 3 + 3 + 4 + 4 + 4 + 4) x^{8} + \dots\dots\dots\dots$ .
Co-efficient of $x^{8} = 29$

Q. The coefficient of x8 in the expression (2+x)2(3+x)3(4+x)4 must be

26

27

28

29

The expression (2+x)2(3+x)3(4+x)4 =(x+2)(x+2)(x+3)(x+3)(x+3)(x+4)(x+4)(x+4)(x+4) =x9+(2+2+3+3+3+4+4+4+4)x8+…………. Co-efficient of x8=29

Q. The coefficient of $x^{8}$ in the expression $(2 + x)^{2} (3 + x)^{3} (4 + x)^{4}$ must be

The expression $(2 + x)^{2} (3 + x)^{3} (4 + x)^{4}$
$= (x + 2) (x + 2) (x + 3) (x + 3) (x + 3) (x + 4) (x + 4) (x + 4) (x + 4)$
$= x^{9} + (2 + 2 + 3 + 3 + 3 + 4 + 4 + 4 + 4) x^{8} + \dots\dots\dots\dots$ .
Co-efficient of $x^{8} = 29$