All categories

3 years ago

15 points for 1 question??

Mathematics

1 answer:

mestny [16]3 years ago

5 0

Answer:a7b2-ab2

Final result :

ab2•(a+1)•(a2-a+1)•(a-1)•(a2+a+1)

Step by step solution :

Step 1 :

Step 2 :

Pulling out like terms :

2.1 Pull out like factors :

a7b2 - ab2 = ab2 • (a6 - 1)

Trying to factor as a Difference of Squares :

2.2 Factoring: a6 - 1

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A2 - AB + BA - B2 =

A2 - AB + AB - B2 =

A2 - B2

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 1 is the square of 1

Check : a6 is the square of a3

Factorization is : (a3 + 1) • (a3 - 1)

Trying to factor as a Sum of Cubes :

2.3 Factoring: a3 + 1

Theory : A sum of two perfect cubes, a3 + b3 can be factored into :

(a+b) • (a2-ab+b2)

Proof : (a+b) • (a2-ab+b2) =

a3-a2b+ab2+ba2-b2a+b3 =

a3+(a2b-ba2)+(ab2-b2a)+b3=

a3+0+0+b3=

a3+b3

Check : 1 is the cube of 1

Check : a3 is the cube of a1

Factorization is :

(a + 1) • (a2 - a + 1)

Trying to factor by splitting the middle term

2.4 Factoring a2 - a + 1

The first term is, a2 its coefficient is 1 .

The middle term is, -a its coefficient is -1 .

The last term, "the constant", is +1

Step-1 : Multiply the coefficient of the first term by the constant 1 • 1 = 1

Step-2 : Find two factors of 1 whose sum equals the coefficient of the middle term, which is -1 .

-1 + -1 = -2

1 + 1 = 2

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Trying to factor as a Difference of Cubes:

2.5 Factoring: a3-1

Theory : A difference of two perfect cubes, a3 - b3 can be factored into

(a-b) • (a2 +ab +b2)

Proof : (a-b)•(a2+ab+b2) =

a3+a2b+ab2-ba2-b2a-b3 =

a3+(a2b-ba2)+(ab2-b2a)-b3 =

a3+0+0+b3 =

a3+b3

Check : 1 is the cube of 1

Check : a3 is the cube of a1

Factorization is :

(a - 1) • (a2 + a + 1)

Trying to factor by splitting the middle term

2.6 Factoring a2 + a + 1

The first term is, a2 its coefficient is 1 .

The middle term is, +a its coefficient is 1 .

The last term, "the constant", is +1

Step-1 : Multiply the coefficient of the first term by the constant 1 • 1 = 1

Step-2 : Find two factors of 1 whose sum equals the coefficient of the middle term, which is 1 .

-1 + -1 = -2

1 + 1 = 2

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Final result :

ab2•(a+1)•(a2-a+1)•(a-1)•(a2+a+1)

Step-by-step explanation:

You might be interested in

the length of a rectangle is five feet less than its width. If the area of the rectangle is 84 square feet, find its dimensions

KIM [24]

Let
x---------> the length of the rectangle
y--------> the width of the rectangle

we know that
A=84 ft²
[area of rectangle]=x*y-----> 84=x*y-----> equation 1
x=y-5------> equation 2
substitute 2 in 1
84=[y-5]*y-----> 84=y²-5y---------> y²-5y-84=0

using a graph tool-----> to resolve the second order equation
see the attached figure

the solution is
y=12
x=y-5-----> x=12-5-----> x=7

the answer is
the length of the rectangle is 7 ft
the width of the rectangle is 12 ft

6 0

3 years ago

Given sec theta=-4/3 and 90

KATRIN_1 [288]

What is ur question?

8 0

3 years ago

Kevin and Randy Muise have a jar containing 84 coins, all of which are either quarters or nickels. The total value of the coins

ella [17]

Dm for the answer can’t do it right now

4 0

3 years ago

Please help !! Picture provided !!!

adelina 88 [10]

Method One
Your calculator might be able to do this. Mine does it like this.
6
nCr
2
=
15

Method 2
You could simply set up 6C2

This gives you
$\frac{n!}{(n- r)! r!} = \frac{6!}{(6 - 2)!2!} = \frac{6!}{4! 2!} = \frac{6*5}{2*1} = 15$

Method Three
You only have to do this a couple of times to see how the cancellation works.

$\frac{6!}{4!2!} = \frac{6*5*\st{4*3*2*1}}{4*3*2*1 * 2*1}$
After all the cancellation takes place you have
6*5/2 = 15

7 0

3 years ago

Can someone help me understand how to do multi-step inequalities please??

tangare [24]

Answer:

In the last two sections, we considered very simple inequalities which required one-step to obtain the solution. However, most inequalities require several steps to arrive at the solution. As with solving equations, we must use the order of operations to find the correct solution. In addition remember that when we multiply or divide the inequality by a negative number the direction of the inequality changes.

The general procedure for solving multi-step inequalities is as follows.

Clear parenthesis on both sides of the inequality and collect like terms.

Add or subtract terms so the variable is on one side and the constant is on the other side of the inequality sign.

Multiply and divide by whatever constants are attached to the variable. Remember to change the direction of the inequality if you multiply or divide by a negative number.

Step-by-step explanation:

8 0

3 years ago