Multiplication of Polynomials | CK-12 Foundation - Free Printable

Here are the solutions for each problem. I have expanded each expression by multiplying the terms step-by-step.

1. $(x + 2)(x - 3)$
* Multiply $x$ by $x$: $x^2$
* Multiply $x$ by $-3$: $-3x$
* Multiply $2$ by $x$: $+2x$
* Multiply $2$ by $-3$: $-6$
* Combine like terms ($-3x + 2x = -x$):
$x^2 - x - 6$

2. $(2y - 1)(y - 2)$
* Multiply $2y$ by $y$: $2y^2$
* Multiply $2y$ by $-2$: $-4y$
* Multiply $-1$ by $y$: $-y$
* Multiply $-1$ by $-2$: $+2$
* Combine like terms ($-4y - y = -5y$):
$2y^2 - 5y + 2$

3. $(x - 1)(x - 1)$
* Multiply $x$ by $x$: $x^2$
* Multiply $x$ by $-1$: $-x$
* Multiply $-1$ by $x$: $-x$
* Multiply $-1$ by $-1$: $+1$
* Combine like terms ($-x - x = -2x$):
$x^2 - 2x + 1$

4. $(x - 2)(x + 2)$
* Multiply $x$ by $x$: $x^2$
* Multiply $x$ by $2$: $+2x$
* Multiply $-2$ by $x$: $-2x$
* Multiply $-2$ by $2$: $-4$
* The middle terms cancel out ($2x - 2x = 0$):
$x^2 - 4$

5. $(2x - 5)(x - 1)$
* Multiply $2x$ by $x$: $2x^2$
* Multiply $2x$ by $-1$: $-2x$
* Multiply $-5$ by $x$: $-5x$
* Multiply $-5$ by $-1$: $+5$
* Combine like terms ($-2x - 5x = -7x$):
$2x^2 - 7x + 5$

6. $(3 - y)(2 - y)$
* Multiply $3$ by $2$: $6$
* Multiply $3$ by $-y$: $-3y$
* Multiply $-y$ by $2$: $-2y$
* Multiply $-y$ by $-y$: $+y^2$
* Combine like terms ($-3y - 2y = -5y$) and rearrange:
$y^2 - 5y + 6$

7. $(x - 2)(y - 3)$
* Multiply $x$ by $y$: $xy$
* Multiply $x$ by $-3$: $-3x$
* Multiply $-2$ by $y$: $-2y$
* Multiply $-2$ by $-3$: $+6$
* There are no like terms to combine:
$xy - 3x - 2y + 6$

8. $(2x - 3)(3x - 1)$
* Multiply $2x$ by $3x$: $6x^2$
* Multiply $2x$ by $-1$: $-2x$
* Multiply $-3$ by $3x$: $-9x$
* Multiply $-3$ by $-1$: $+3$
* Combine like terms ($-2x - 9x = -11x$):
$6x^2 - 11x + 3$

9. $(y - 2x)(y - x)$
* Multiply $y$ by $y$: $y^2$
* Multiply $y$ by $-x$: $-xy$
* Multiply $-2x$ by $y$: $-2xy$
* Multiply $-2x$ by $-x$: $+2x^2$
* Combine like terms ($-xy - 2xy = -3xy$) and rearrange:
$2x^2 - 3xy + y^2$

10. $(x - 1)(4 - x)$
* Multiply $x$ by $4$: $4x$
* Multiply $x$ by $-x$: $-x^2$
* Multiply $-1$ by $4$: $-4$
* Multiply $-1$ by $-x$: $+x$
* Combine like terms ($4x + x = 5x$) and rearrange:
$-x^2 + 5x - 4$

Final Answer:
1. $x^2 - x - 6$
2. $2y^2 - 5y + 2$
3. $x^2 - 2x + 1$
4. $x^2 - 4$
5. $2x^2 - 7x + 5$
6. $y^2 - 5y + 6$
7. $xy - 3x - 2y + 6$
8. $6x^2 - 11x + 3$
9. $2x^2 - 3xy + y^2$
10. $-x^2 + 5x - 4$