Question

Factorise x(y+z)(y²+z²-x²)+y(z+x)(z²+x²-y²)+ z(x+y)(x²+y²-z²)

Answer 1

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "z2" was replaced by "z^2". 8 more similar replacement(s).

Step by step solution : Step 1 : Equation at the end of step 1 : (((x•(y+z))•(((y²)+(z²))-(x²)))+((y•(x+z))•(((z²)+(x²))-(y²))))+(z•(x+y)•(x²+y²-z²)) Step 2 : Trying to factor a multi variable polynomial :

2.1 Factoring x² + y² - z²

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

Factorization fails

Equation at the end of step 2 : (((x•(y+z))•(((y²)+(z²))-(x²)))+((y•(x+z))•(((z²)+(x²))-(y²))))+z•(x+y)•(x²+y²-z²) Step 3 : Equation at the end of step 3 : (((x•(y+z))•(((y²)+(z²))-(x²)))+(y•(x+z)•(x²-y²+z²)))+z•(x+y)•(x²+y²-z²) Step 4 : Trying to factor a multi variable polynomial :

4.1 Factoring x² - y² + z²

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

Factorization fails

Equation at the end of step 4 : (((x•(y+z))•(((y²)+(z²))-(x²)))+y•(x+z)•(x²-y²+z²))+z•(x+y)•(x²+y²-z²) Step 5 : Equation at the end of step 5 : ((x•(y+z)•(-x²+y²+z²))+y•(x+z)•(x²-y²+z²))+z•(x+y)•(x²+y²-z²) Step 6 : Trying to factor a multi variable polynomial :

6.1 Factoring -x² + y² + z²

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

Factorization fails

Equation at the end of step 6 : (x•(y+z)•(-x²+y²+z²)+y•(x+z)•(x²-y²+z²))+z•(x+y)•(x²+y²-z²) Step 7 : Step 8 : Pulling out like terms :

8.1 Pull out like factors :

2x²yz + 2xy²z + 2xyz² = 2xyz • (x + y + z)

Final result : 2xyz • (x + y + z)