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Ksenya-84 [330]
2 years ago
13

Expand the binomial (4x + 3y)3. The coefficient of the second term in the expansion of the binomial (4x + 3y)3

Mathematics
2 answers:
Anettt [7]2 years ago
4 0
The answer is, 12x +9y
jonny [76]2 years ago
3 0

Answer:

The coefficient is 144.

Step-by-step explanation:

We have the binomial: (4x+3y)^3

The general formula for cubic binomials is:

(a+b)^3=a^3+3a^2b+3ab^2+b^3\\\\(a-b)^3=a^3-3a^2b+3ab^2-b^3

<em>Observation: (a+b)^3=(a+b)(a+b)(a+b) if you solve that the result is the general formula. The same for  (a-b)^3=(a-b)(a-b)(a-b) </em>

Then we have:

(4x+3y)^3=(4x)^3+3(4x)^2.(3y)+3(4x).(3y)^2+(3y)^3\\\\=64x^3+3.16x^2.3y+3.4x.9y^2+27y^3\\\\=64x^3+144x^2y+108xy^2+27y^3

The coefficient is the number before the variable, then the coefficient of the second term in the expansion of the binomial (4x+3y)^3 is 144.

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