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maksim [4K]
3 years ago
14

The last term in the expansion of the binomial (3x+6)^3 is?

Mathematics
2 answers:
kolbaska11 [484]3 years ago
7 0
The last term will be the second part cubed or 6^3 which equals 216
vivado [14]3 years ago
3 0
1. Use Cube of sum : (a+b)^3 = a^3+3a^2b+3ab^2+b^3
(3x+6)((3x)^2+2*3x*6+6^2)

2. Use multiplication distributive property (xy)^a=x^ay^a
(3x+6)(3^2x^2+2*3x+6+6^2)

3. Simplify 3^2 to 9
(3x+6)(9X^2+2*3X*6+6^2)

4. Simplify 6^2 to 36
(3x+6)(9x^2+2*3x*6+36)

5. Simplify 2*3x*6 to 36x
(3x+6)(9x^2+36x+36)

6. Distribute sum groups
3x(9x^2+36x+36)+6(9x^2+36x+36)

7. Distribute
27x^3+108x^2+108x+6(9x^2+36x+36)

8. Distribute 
27x^3+108x^2+108x+54x^2+216x+216

9. Collect like terms
27x^3+(108x^2+54x^2)+(108x+216x)+216

10. Simplify 
27x^3+162x^2+324x+216

The last term is therefore, 216. Have a nice day :D
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Considering the vertex of the quadratic function, it is found that:

A robot traveling along the surface of the curved pit reaches a minimum depth of -22.25 feet.

<h3>What is the vertex of a quadratic equation?</h3>

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The vertex is given by:

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Considering the coefficient a, we have that:

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In this problem, the function is given by:

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Which means that the coefficients are a = 0.75 > 0, b = -13.5, c = 57.75.

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More can be learned about the vertex of a quadratic function at brainly.com/question/24737967

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