A polynomial is expanded if no variable appears within parentheses and all like terms have been combined.
To expand a polynomial, multiply its factors (often by using the distributive property) or perform the indicated operations. Then combine all like terms.
Expand the following expression.
3x(4 - x) + (2x - 5)2
Remembering the order of operations, we take care of exponents before multiplication.
Because (2x - 5)2 = (2x - 5)(2x - 5), recall that we can use the FOIL method to multiply this out, then combine like terms:
(2x - 5)(2x - 5) = 4x2 - 10x - 10x + 25
= 4x2 - 20x + 25
Now we have:
3x(4 - x) + (4x2 - 20x + 25)
Multiply the 3x by (4 - x) using the distributive property:
(12x - 3x2) + (4x2 - 20x + 25)
Now all that's left is to add the polynomials by combining like terms. Remember, when complete, the polynomial is written in standard form, so the exponents are in descending order:
(12x - 3x2) + (4x2 - 20x + 25) = -8x + x2 + 25 = x2 - 8x + 25
1) (x + 1)(x - 1)(x - 3)
2) (2x + 3y)2
3) (3x + 3)(6x - 6)
4) (x2 - 2x + 3)2
5) (x + 1)5
6) (x - 1)6