Expand (x+2)^6 using the Binomial Theorem and Pascal’s triangle. Show your work.

x⁶ + 12x⁵ + 60x⁴ + 160x³ + 240x² + 192x + 64

Step-by-step explanation:

We shall expand the brackets;

(x + 2)^6

x⁶ + x⁵2 + x⁴2² + x³2³ + x²2⁴ + x2⁵ + 2⁶

x⁶ + 2x⁵ + 4x⁴ + 8x³ + 16x² + 32x + 64

We shall then use Pascal’s triangle to fit in the coefficients;

(1) x⁶ + (6) 2x⁵ + (15) 4x⁴ + (20) 8x³ + (15) 16x² + (6) 32x + (1) 64

x⁶ + 12x⁵ + 60x⁴ + 160x³ + 240x² + 192x + 64

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