Solve Powerequation (10x^4y^3+5x^3y^2-15x^2y-25x^2y^4)

Reformatting the input :

Changes made to your input should not affect the solution: (1): "/-5x" was replaced by "/(-5x)".

Step 1 :

1.1 Negative number raised to an even power is positive

For example let's look at (-7)6 , where (-7) , a negative number, is raised to 6 , an even exponent :(-7)6 can be written as (-7)•(-7)•(-7)•(-7)•(-7)•(-7)Now, using the rule that says minus times minus is plus, (-7)6 can be written as (49)•(49)•(49) which in turn can be written as (7)•(7)•(7)•(7)•(7)•(7) or 76 which is positive. We proved that (-7)6 is equal to (7)6 which is a positive number Using the same arguments as above, replacing (-7) by any negative number, and replacing the exponent 6 by any even exponent, we proved which had to be proved

Equation at the end of step 1 :

(((((10•(x4))•(y3))+((5•(x3))•(y2)))-((15•(x2))•y))-((25•(x2))•(y4))) —————————————————————————————————————————————————————————————————————•y 52x2

Step 2 :

Equation at the end of step 2 :

(((((10•(x4))•(y3))+((5•(x3))•(y2)))-((15•(x2))•y))-(52x2•y4)) ——————————————————————————————————————————————————————————————•y 52x2

Step 3 :

Equation at the end of step 3 :

(((((10•(x4))•(y3))+((5•(x3))•(y2)))-((3•5x2)•y))-52x2y4) —————————————————————————————————————————————————————————•y 52x2

Step 4 :

Equation at the end of step 4 :

(((((10•(x4))•(y3))+(5x3•y2))-(3•5x2y))-52x2y4) ———————————————————————————————————————————————•y 52x2

Step 5 :

Equation at the end of step 5 :

(((((2•5x4)•y3)+5x3y2)-(3•5x2y))-52x2y4) ————————————————————————————————————————•y 52x2

Step 6 :

10x4y3 + 5x3y2 - 25x2y4 - 15x2y Simplify ——————————————————————————————— 52x2

Step 7 :

Pulling out like terms :

7.1 Pull out like factors : 10x4y3 + 5x3y2 - 25x2y4 - 15x2y = 5x2y • (2x2y2 + xy - 5y3 - 3)

Checking for a perfect cube :

7.2 2x2y2 + xy - 5y3 - 3 is not a perfect cube

Canceling Out :

7.3 Canceling out x2 as it appears on both sides of the fraction line

Dividing exponents :

7.4 51 divided by 52 = 5(1 - 2) = 5(-1) = 1/51 = 1/5

Equation at the end of step 7 :

y • (2x2y2 + xy - 5y3 - 3) —————————————————————————— • y 5

Step 8 :

Multiplying exponential expressions :

8.1 y1 multiplied by y1 = y(1 + 1) = y2

Final result :

y2 • (2x2y2 + xy - 5y3 - 3) ——————————————————————————— 5