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2 years ago

Find the following expression by multiplying (A+b)^3

Mathematics

1 answer:

DaniilM [7]2 years ago

8 0

Given expression: (A+b)^3.

We can expand it into three factors as (A+b)(A+b)(A+b).

First we would foil (A+b)(A+b) = $A^2 + Ab+Ab+ b^2$

Combining like terms, we get

= $A^2 +2Ab + b^2$

Now, we would multiply (A^2 +2Ab + b^2) and (A+b).

= $A^3 + A^2b + 2A^2b+2Ab^2 + Ab^2+ b^3$

Combining like terms, we get

$=A^3+3A^2b+3Ab^2+b^3$

Therefore,

$\left(A+b\right)^3=\quad A^3+3A^2b+3Ab^2+b^3$

You might be interested in

6,666,666×666,666 /1+2+3+4+5+6+5+4+3+2+1 − 777,777×777,777/1+2+3+4+5+6+7+6+5+4+3+2+1

jeka57 [31]

Answer:

111111 $\times$ 1111110 is the simple expression.

Step-by-step explanation:

The expression to be solved:

$\dfrac{6,666,666\times666,666 }{1+2+3+4+5+6+5+4+3+2+1} - \dfrac{777,777\times777,777}{1+2+3+4+5+6+7+6+5+4+3+2+1}$

First of all, let us solve the first term:

$\dfrac{6,666,666\times666,666 }{1+2+3+4+5+6+5+4+3+2+1}\\\Rightarrow \dfrac{6666666\times666666 }{36}\\\Rightarrow \dfrac{6666666\times666666 }{6\times 6}\\\Rightarrow 1111111\times 111111$

Now, the right term:

$\dfrac{777777\times777777}{1+2+3+4+5+6+7+6+5+4+3+2+1}\\\Rightarrow \dfrac{777777\times777777}{49}\\\Rightarrow \dfrac{777777\times777777}{7 \times 7}\\\Rightarrow 111111 \times 111111$

So, the expression to be solved becomes:

$1111111\times 111111-111111\times 111111\\\Rightarrow 111111(1111111-1)\\\Rightarrow 111111\times 1111110$

3 0

2 years ago

Can someone please answer this???? ASAP

timofeeve [1]

Answer:

A. $y=-\dfrac{8}{7}x-\dfrac{18}{7}$

Step-by-step explanation:

Let $y=mx+b$ be the equation of the perpendicular line.

Two perpendicular lines have slopes with product equal to -1. The slope of the given line is $\frac{7}{8}$ Hence,

$\dfrac{7}{8}\cdot m=-1\\ \\m=-\dfrac{8}{7}$

is the slope of needed line.

This line passes through the point (-4,2), so its coordinates satisfy the equation:

$2=-\dfrac{8}{7}\cdot (-4)+b\\ \\b=2-\dfrac{32}{7}=-\dfrac{18}{7}$

Therefore, the equation of the line is

$y=-\dfrac{8}{7}x-\dfrac{18}{7}$

7 0

2 years ago

P is the point on the line 2x+y-10=0 such that the length of OP, the line segment from the origin O to P, is a minimum. Find the

nirvana33 [79]

The minimum distance is the perpendicular distance. So establish the distance from the origin to the line using the distance formula.
The distance here is: d2=(x−0)^2+(y−0)^2
 =x^2+y^2

To minimize this function d^2 subject to the constraint, 2x+y−10=0
If we substitute, the y-values the distance function can take will be related to the x-values by the line:y=10−2x
You can substitute this in for y in the distance function and take the derivative:
d=sqrt [x2+(10−2x)^2]

d′=1/2 (5x2−40x+100)^(−1/2) (10x−40)
Setting the derivative to zero to find optimal x,
d′=0→10x−40=0→x=4

This will be the x-value on the line such that the distance between the origin and line will be EITHER a maximum or minimum (technically, it should be checked afterward).
For x = 4, the corresponding y-value is found from the equation of the line (since we need the corresponding y-value on the line for this x-value).

Then y = 10 - 2(4) = 2.
So the point, P, is (4,2).

8 0

3 years ago

Please help I need for graph

Gala2k [10]

For a you will see a bar graph and the dependent o think would be bird species

3 0

2 years ago

Yall please help me i need to turn this in asap

Monica [59]

Answer:

A)9

Step-by-step explanation:

so if we see the figure the angle are vertical opposite

and so are equal ,

3x+8=35

3x=35-8

3x=27

x=27/3

x=9

hope it helps

8 0

2 years ago