Question

When (x+1)^4 is expanded and like terms are combined what is the coefficients of x^2

Answer 1

(x+1)^4

(x+1)²(x+1)²

(x²+2x+1)(x²+2x+1)

x²(x²+2x+1)+2x(x²+2x+1)+1(x²+2x+1)

x⁴+2x³+x²+2x³+4x²+2x+x²+2x+1

x⁴+4x³+6x²+4x+1

coefficient of x²=6

Answer 2

• 6

Explanation:

Expand (x + 1)⁴:

• (x + 1)⁴ =
• ((x + 1)(x + 1))² =
• (x² + 2x + 1)² =
• (x² + 2x + 1)(x² + 2x + 1) =
• x²(x²) + x²(2x) + x²(1) + 2x(x²) + 2x(2x) + 2x(1) + 1(x²) + 1(2x) + 1(1) =
• x⁴ + 2x³ + 2x² + 2x³ + 4x² + 4x + 1 =
• x⁴ + 4x³ + 6x² + 4x + 1

The coefficient of x² is 6