Based on the fact that it should be a binomial with coefficients other than one, the binomial would be (2x + 3y) and the expansion of that binomial would be (2x + 3y)⁶ = 64x + 576x⁵y + 2,160x⁴y⁶ + 4,320x³y³ + 4,860x²y⁴ + 2,916xy⁵ + 729y₆.
<h3>How can the binomial be expanded?</h3>
The binomial chosen is (2x + 3y) which involves coefficients that aren't one. The numbers chosen are instead those closest to one for ease of calculation.
Expanding the binomial to the 6th power means to multiply the binomial by itself six times.
In equation form, the binomial would turn out as:
(2x + 3y)⁶
To expand it to the 6th power, assume that:
6c₀ = 1
6c₁ = 6
6c₂ = 15
6c₃ = 20
6c₄ = 15
6c₅ = 6
6c₆ = 1
Expansion gives:
(2x + 3y)⁶ = (64x) + 6(32x⁵)(3y) + 15(16x⁴)(9y²) + 20 (8x³)(27y³) + 15(4x²)(81y⁴) + 6(2x)(243y⁵) + 1 (729y⁶)
(2x + 3y)⁶ = 64x + 576x⁵y + 2,160x⁴y⁶ + 4,320x³y³ + 4,860x²y⁴ + 2,916xy⁵ + 729y₆
Find out more on expanding binomials at brainly.com/question/17154383
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