Answer:
x³ - 2x²y + 3xy² - y³
Explanation:
When multiplying with two brackets, you need to multiply the two terms, (x) and (-y) from the first bracket to all the terms in the second brackets, (x²), (-2xy) and (y²) individually. I have put each multiplied term in a bracket so it is easier.
(x-y)(x²-2xy+y²) =
(x × x²) + {x × (-2xy)} + (x × y²) + {(-y) × x²) + {(-y) × (-2xy)} + {(-y) × y²)
Now we can evaluate the terms in the brackets.
(x × x²) + {x × (-2xy)} + (x × y²) + {(-y) × x²) + {(-y) × (-2xy)} + {(-y) × y²) =
(x³) + (-2x²y) + (xy²) + (2xy²) + (-y³)
We can open the brackets now. One plus and one minus makes a minus.
(x³) + (-2x²y) + (xy²) + (2xy²) + (-y³) = x³ - 2x²y + xy² + 2xy² - y³
Evaluate like terms.
x³ - 2x²y + xy² + 2xy² - y³ = x³ - 2x²y + 3xy² - y³