Algebraic expansion practice worksheet with questions and discussion points.

1) $x^2 + 4x$
2) $4x + x^2$
3) $4x - x^2$
4) $x^2 - 4x$
5) $-x^2 - 4x$
6) $-x^2 - 4x$
7) $-x^2 + 4x$
8) $-2x^2 + 4x$
9) $-4x + 2x^2$
10) $-6x + 3x^2$
11) $3x^2 - 6x$
12) $3x^2 - 6xy$
13) $15x^2 - 6xy$
14) $-6xy + 15x^2$
15) $-6x^2y + 15x^3$
16) $-6y^3 + 15xy^2$
17) $-6y^3 + 15xy^3$
18) $-6y^3 + 15xy^3$

- The answer to questions 1 and 2 is the same because addition is commutative; $x(x+4)$ and $x(4+x)$ are identical expressions, so their expansions are identical.
- The answer to questions 5 and 6 is the same because both expressions simplify to $-x^2 - 4x$. For question 5, $x(-x - 4) = -x^2 - 4x$. For question 6, $-x(x + 4) = -x^2 - 4x$.
- The answer to questions 17 and 18 is the same because both expressions simplify to $-6y^3 + 15xy^3$. For question 17, $-3y^2(2y - 5xy) = -6y^3 + 15xy^3$. For question 18, $-3y^3(2 - 5x) = -6y^3 + 15xy^3$.