The expansion of (x+3)⁷ using the binomial theorem is x⁷ + 21x⁶ + 189x⁵ + 945x⁴ + 2835x³ + 5103x² + 5103x + 2187
To write the coefficients of the 8 terms, either start with a combination of 7 things taken 0 at a time and continue to 7 things taken 7 at a time or use the 7th row of Pascal’s triangle.
For the first term, write x to the 7th power and 3 to the 0 power. Then decrease the power on x and increase the power on y until you reach x to the 0 and y to the 7.
Using binomial theorem,
(x+3)⁷ = ⁷C₀ (x)⁷(3)⁰ + ⁷C₁ (x)⁶ (3)¹ + ⁷C₂ (x)⁵ (3)² + ⁷C₃ (x)⁴ (3)³ + ⁷C₄ (x)³ (3)⁴ + ⁷C₅ (x)² (3)⁵ + ⁷C₆ (x)¹ (3)⁶ + ⁷C₇ (x)⁰ (3)⁷
= x⁷ + 21x⁶ + 189x⁵ + 945x⁴ + 2835x³ + 5103x² + 5103x + 2187
To learn more about binomial theorem from the given link
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