Expand and simplify (x + 5y)(2x - y).

Step-by-step solution

1. 1

   Distribute the first term of the left bracket. Multiply $x$ by each term of $(2x-y)$:

   $x(2x-y)=2x^2-xy$

2. 2

   Distribute the second term. Now multiply $5y$ by each term, watching the sign on $-y$:

   $5y(2x-y)=10xy-5y^2$

   Here $5y\cdot(-y)=-5y^2$, not $-5y$ — multiplying two $y$ factors raises the power.

3. 3

   Add the four terms.

   $2x^2-xy+10xy-5y^2$

4. 4

   Combine the like terms. Only the two $xy$ terms are alike; $x^2$ and $y^2$ have no partners:

   $-xy+10xy=9xy\quad\Longrightarrow\quad 2x^2+9xy-5y^2$

5. 5

   Check with a substitution. At $x=1$, $y=2$: the original is $(1+10)(2-2)=11\cdot 0=0$, and the expansion gives $2+18-20=0$ $\checkmark$. A second test at $x=2$, $y=1$: $(2+5)(4-1)=21$, and $8+18-5=21$ $\checkmark$.