79.5k views
1 vote
- 8x + 40 - 8x - 35​

1 Answer

6 votes

Final result :

-4x40 - 40x - 175

—————————————————

5

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "x4" was replaced by "x^4".

(2): ".8" was replaced by "(8/10)".

Step by step solution :

Step 1 :

4

Simplify —

5

Equation at the end of step 1 :

4

((0 - (— • x40)) - 8x) - 35

5

Step 2 :

Equation at the end of step 2 :

4x40

((0 - ————) - 8x) - 35

5

Step 3 :

Rewriting the whole as an Equivalent Fraction :

3.1 Subtracting a whole from a fraction

Rewrite the whole as a fraction using 5 as the denominator :

8x 8x • 5

8x = —— = ——————

1 5

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

3.2 Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

-4x40 - (8x • 5) -4x40 - 40x

———————————————— = ———————————

5 5

Equation at the end of step 3 :

(-4x40 - 40x)

————————————— - 35

5

Step 4 :

Rewriting the whole as an Equivalent Fraction :

4.1 Subtracting a whole from a fraction

Rewrite the whole as a fraction using 5 as the denominator :

35 35 • 5

35 = —— = ——————

1 5

Step 5 :

Pulling out like terms :

5.1 Pull out like factors :

-4x40 - 40x = -4x • (x39 + 10)

Trying to factor as a Sum of Cubes :

5.2 Factoring: x39 + 10

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 : 10 is not a cube !!

Ruling : Binomial can not be factored as the difference of two perfect cubes

Adding fractions that have a common denominator :

5.3 Adding up the two equivalent fractions

-4x • (x39+10) - (35 • 5) -4x40 - 40x - 175

————————————————————————— = —————————————————

5 5

Step 6 :

Pulling out like terms :

6.1 Pull out like factors :

-4x40 - 40x - 175 = -1 • (4x40 + 40x + 175)

Final result :

-4x40 - 40x - 175

—————————————————

5

User Syneryx
by
8.4k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories