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3 years ago

Expand the binomial (a+2)^4

Mathematics

2 answers:

sp2606 [1]3 years ago

6 0

Answer: $a^4+8a^3+24a^2+32a+16$

Step-by-step explanation:

The binomial expansion of $(a+b)^n=^nC_0a^nb^{0}+^nC_1a^{n-1}b^1+^nC_2a^{n-2}b^2+.........+^nC_na^0b^n$

For $(a+2)^4$ , n=4 and b= 2 , we have

Then, the binomial expansion of $(a+2)^4$ will be :

$(a+2)^4=^4C_0a^4(2)^{0}+^4C_1a^{4-1}2^1+^4C_2a^{4-2}2^2++^4C_3a^{4-3}2^3++^4C_4a^{0}2^4\\\\=(1)a^4+(4)a^3(2)+\dfrac{4!}{2!(4-2)!}a^2(4)+(4)a(8)+(1)(16)$

∵ $^nC_0=^nC_n=0$ and $^nC_1=^nC_{n-1}=n$

$=a^4+8a^3+(6)a^2(4)+32a+16\\\\=a^4+8a^3+24a^2+32a+16$

Hence, the binomial expansion of $(a+2)^4=a^4+8a^3+24a^2+32a+16$

dimaraw [331]3 years ago

4 0

Answer:

Step-by-step explanation:

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the weight M of an object on Mars varies directly as it’s weight E on Earth. A person who weighs 95 lb on Earth weighs 38 lb on

lorasvet [3.4K]

Answer:

A 100 lb person will weight 40 lb on Mars

Step-by-step explanation:

Given:

Weight on Mars directly varies as its weight on earth.

Let weight on Mars be = $M$

Let weight on Earth be = $E$

Its known that:

$M$ ∝ $E$

Thus

$M=kE$

where $k$ is constant of proportionality.

when $E=95\ lb$ , then $M=38\ lb$

thus, we have

$38=k(95)$

dividing both sides by 95.

$\frac{38}{95}=\frac{k(95)}{95}$

∴ $k=\frac{38}{95}$

Thus when $E= 100$ , $M$ would be calculated as

$M=\frac{38}{95}\times 100$

$M=\frac{3800}{95}$

∴ $M=40\ lb$ (Answer)

∴ A 100 lb person will weight 40 lb on Mars.

8 0

3 years ago

I REALLY NEED AN ANSWER FAST! Which statement about the diagram is true?

Marina86 [1]

Answer:

Step-by-step explanation:

To keep it short, refer to triangle exterior angle theorem.

Edit: If you want the full explanation,

A isn't the answer. The triangle exterior angle states that the measure of the 2 triangle interior add up to the the exterior angle of the other interior angle within the triangle.

Meaning that

measure of angle 1 equal the measure of 3 and 4 combined.

B. is wrong they are equal to each other because angle 2 is equal to angle 2

angle 1 is equal to angle 3 and 4

So they are equal

C.Wrong unless it a 30 60 90 triangle or 45 45 90 triangle, C is wrong

D. is right since measure of angle 4 and angle 3 add up to angle 1, angle 4 would be lesser than angle 1.