Question

Add the following : xy - 4x , 4y - xy , 4x - 4y​

Answer 1

Answer:

We think you wrote:

4x-4y/x-y

This deals with reducing fractions to their lowest terms.

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Step by Step Solution

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STEP

1

:

y

Simplify —

x

Equation at the end of step

1

:

y

(4x - (4 • —)) - y

x

STEP

2

:

Rewriting the whole as an Equivalent Fraction

2.1 Subtracting a fraction from a whole

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

4x 4x • x

4x = —— = ——————

1 x

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 :

2.2 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:

4x • x - (4y) 4x2 - 4y

————————————— = ————————

x x

Equation at the end of step

2

:

(4x2 - 4y)

—————————— - y

x

STEP

3

:

Rewriting the whole as an Equivalent Fraction :

3.1 Subtracting a whole from a fraction

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

y y • x

y = — = —————

1 x

STEP

4

:

Pulling out like terms :

4.1 Pull out like factors :

4x2 - 4y = 4 • (x2 - y)

Trying to factor as a Difference of Squares:

4.2 Factoring: x2 - y

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 : x2 is the square of x1

Check : y1 is not a square !!

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

Adding fractions that have a common denominator :

4.3 Adding up the two equivalent fractions

4 • (x2-y) - (y • x) 4x2 - xy - 4y

———————————————————— = —————————————

x x

Trying to factor a multi variable polynomial :

4.4 Factoring 4x2 - xy - 4y

Try to factor this multi-variable trinomial using trial and error

Factorization fails

Final result :

4x2 + xy + 4y

—————————————

x

Step-by-step explanation:

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Answer 2

Answer:

0

Step-by-step explanation:

xy - 4x

-xy + 4y

4x - 4y

xy - xy = 0

+4y - 4y = 0

-4x + 4x = 0

So , 0 + 0 + 0 = 0