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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:

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Alternate Hypothesis, $H_A$ : $\mu\neq$ 22 ounces {means that the average different from 22 ounces of passion fruit juice is used to fill each bottle}

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Therefore, we conclude that Reject $H_0$ since the value of the test statistic is less than the negative critical value which means that the average different from 22 ounces of passion fruit juice is used to fill each bottle.

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