SOLUTION: Expand and simplify: (x+y-z) (x-y+z) Could you please have a step by step solution? It's really hard to me, thanks!

Question 1016732: Expand and simplify:
(x+y-z) (x-y+z)
Could you please have a step by step solution? It's really hard to me, thanks!
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
(x + y - z) * (x - y + z)

you use the distributive law of multiplication.
that law says that each element in the multiplier needs to multiply each element in the multiplicand exactly one time.

you break your multiplication up as follows:

(x + y - z) * (x - y + z) equals:

x * (x - y + z) + y * (x - y + z) - z * (x - y + z)

x * (x - y + z) is equal to x^2 - xy + xz
y * (x - y + z) is equal to xy - y^2 + yz
- z * (x - y + z) is equal to -xz + yz - z^2

when you put them all together, you get:

x * (x - y + z) + y * (x - y + z) - z * (x - y + z) is equal to:

x^2 - xy + xz + xy - y^2 + yz - xz + yz - z^2

when you combine like terms, you get:

- xy and +xy cancel out.
+ xz and -xz cancel out.
+ yz and + yz becomes 2yz.

you are left with x^2 - y^2 + 2yz - z^2

that's your final expression.

you can confirm you did this correctly by assigning random values to x,y, and z.

i assigned x = 2, y = 3, z = 4.

the original expression is:

(x + y - z) * (x - y + z)

after assigning values, the expression becomes (2 + 3 - 4) * (2 - 3 + 4).
this becomes 1 * 3 which is equal to 3.

the final expression is:

x^2 - y^2 + 2yz - z^2

after assigning values, the expression becomes 2^2 - 3^2 + 2*3*4 - 4^2.
this becomes 4 - 9 + 24 - 16 which is equal to 3.

original expression and final expression give the same answer, therefore they are equivalent.

solution looks good.

your solution is:

(x + y - z) * (x - y + z) = x^2 - y^2 + 2yz - z^2

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