Mathematics High School

What is the coefficients of x4 in the expansion of (1+x)4(1+2x)3.

Answers

Answer 1

By the binomial theorem,

(1 + x)⁴ = 1 + 4x + 6x² + 4x³ + x⁴

(1 + 2x)³ = 1 + 6x + 12x² + 8x³

In the expansion of (1 + x)⁴ (1 + 2x)³, we get an x⁴ when multiplying

• x⁴ and 1 to get x⁴;

• 4x³ and 6x to get 24x⁴;

• 6x² and 12x² to get 72x⁴; and

• 4x and 8x³ to get 32x⁴.

Add these up:

x⁴ + 24x⁴ + 72x⁴ + 32x⁴ = 129x⁴

Related Questions

What is the value of q?
S
415
2/14
S
2015
ין
R
4
64,5
T
10

Answers

Answer:

[tex]2 \sqrt{14} [/tex]

Point P is the center of the circle in the figure above. What is the value of x?

Answers

Answer:

x = 80°

Step-by-step explanation:

To find x, we need to create an equation.

Recall that the sum of all the 4 interior angles of a quadrilateral = 360°.

Therefore:

m<B + m<A + m<C + m<P = 360°

m<B = 20° (given)

m<C = 20° (given)

m<A = ½*x = x/2 (inscribed angle theorem)

m<P = (360 - x)°

Plug in the values and solve for x

[tex] 20 + \frac{x}{2} + 20 + (360 - x) = 360 [/tex]

[tex] 20 + \frac{x}{2} + 20 + 360 - x = 360 [/tex]

Collect like terms

[tex] 20 + 20 + 360 + \frac{x}{2} - x = 360 [/tex]

[tex] 400 + \frac{x}{2} - x = 360 [/tex]

Subtract 400 from each side

[tex] 400 + \frac{x}{2} - x - 400 = 360 - 400 [/tex]

[tex] \frac{x}{2} - x = -40 [/tex]

[tex] \frac{x - 2x}{2} = -40 [/tex]

[tex] \frac{-x}{2} = -40 [/tex]

Multiply both sides by 2

[tex] \frac{-x}{2} \times 2 = -40 \times 2 [/tex]

[tex] -x = -80 [/tex]

Divide both sides by -1

[tex] \frac{-x}{-1} = \frac{-80}{-1} [/tex]

[tex] x = 80 [/tex]

please I need some help with both questions.

Answers

Step-by-step explanation:

which questions you were asking

Can any one help
WILL GIVE 30 POINTS

Answers

The believe the answer is C but I could be wrong, good luck!

Answer:I think it’s b too

Step-by-step explanation:

please help!! I'm confused, ignore the math book thing. And it's asking what property it is, the associative property or the communitive property?

Answers

Answer:

its associative property

Step-by-step explanation:

2+d=2+d

d=2

dudee plz help will be given the brainlist if answered correctly

Answers

Answer:

hey im not actually here to help you, i just need points. thanks for the points

Step-by-step explanation:

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