In Example 3, change the exponent from 6 to 5 Data from Example 3 Using the binomial formula, expand (2x 3) 6 In using the binomial formula for (2x 3) 6 , we use 2x for a, 3 for b, and 6 for n Thus, 6 n 1 I n n 1 n 2 (6)(5) (2x) (3) (2x 3) (2x) 6(2x) (3) (6) (5) (4) (2x) (3) (2)(3) (6)(5)(4)(3) (2)(3)(4) 3 21 4 64x6 576x5 2160x4 4320x3 4860x 2916x 729 (2x) (3) 4 (6)(5)(4)(3)(2), (2)(3)(4)(5) 5 2(2x)(3) (3)6

Question: In Example 3, change the exponent from 6 to 5. Data from Example 3 Using the binomial formula, expand (2x + 3) 6 . In

In Example 3, change the exponent from 6 to 5.

Data from Example 3

Using the binomial formula, expand (2x + 3)⁶. In using the binomial formula for (2x + 3)⁶ , we use 2x for a, 3 for b, and 6 for n. Thus,

=6 n- 1 I n n-1 n - 2 (6)(5) (2x) (3)

=6 n- 1 I n n-1 n - 2 (6)(5) (2x) (3) + (2x+3) = (2x) + 6(2x) (3) +- (6) (5) (4) (2x) (3) + (2)(3) (6)(5)(4)(3) (2)(3)(4) 3! 21 4! = 64x6 + 576x5 + 2160x4 + 4320x3 + 4860x + 2916x + 729 (2x) (3) 4 (6)(5)(4)(3)(2), (2)(3)(4)(5) 5! 2(2x)(3) +(3)6

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