Step by Step Solution
Step 1 :
Equation at the end of step 1 :
((x2)-y)
(((49•(x3))•z)•————————)•(y-x2)
73z3y3
Step 2 :
x2 - y
Simplify ——————
73z3y3
Trying to factor as a Difference of Squares :
2.1 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
Equation at the end of step 2 :
(x2-y) (((49•(x3))•z)•——————)•(y-x2) 73z3y3Step 3 :
Equation at the end of step 3 :
(x2 - y)
((72x3 • z) • ————————) • (y - x2)
73z3y3
Step 4 :
Dividing exponential expressions :
4.1 z1 divided by z3 = z(1 - 3) = z(-2) = 1/z2
Dividing exponents :
4.2 72 divided by 73 = 7(2 - 3) = 7(-1) = 1/71 = 1/7
Equation at the end of step 4 :
x3 • (x2 - y)
————————————— • (y - x2)
7z2y3
Step 5 :
Trying to factor as a Difference of Squares :
5.1 Factoring: y-x2
Check : y1 is not a square !!
Ruling : Binomial can not be factored as the difference of two perfect squares
5.2 Rewrite (y-x2) as (-1) • (x2-y)
Multiplying Exponential Expressions :
5.3 Multiply (x2-y) by (x2-y)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (x2-y) and the exponents are :
1 , as (x2-y) is the same number as (x2-y)1
and 1 , as (x2-y) is the same number as (x2-y)1
The product is therefore, (x2-y)(1+1) = (x2-y)2
Final result :
-x3 • (x2 - y)2
———————————————
7z2y3
How did we do?
Please leave us feedback.