Simplify the algebraic expression 8(5y - 4) + 3(4y + 7).

Step-by-step solution

1. 1

   Distribute the first coefficient across its whole bracket. The $8$ multiplies both terms, including the negative one:

   $8(5y-4)=8\cdot 5y-8\cdot 4=40y-32.$

2. 2

   Distribute the second coefficient. The bracket is preceded by a plus, so no signs flip:

   $3(4y+7)=12y+21.$

3. 3

   Write the expression with the brackets gone.

   $40y-32+12y+21.$

4. 4

   Group like terms. Only terms with the same variable part combine:

   $\underbrace{(40y+12y)}_{y\text{-terms}}+\underbrace{(-32+21)}_{\text{constants}}.$

5. 5

   Combine each group.

   $52y-11.$

   The answer cannot be simplified further: $52y$ and $-11$ are unlike terms, so writing something like $41y$ would be wrong.

6. 6

   Check with a value. At $y=1$ the original is $8(1)+3(11)=8+33=41$, and $52(1)-11=41$ ✓. At $y=0$ the original is $8(-4)+3(7)=-32+21=-11$, matching the constant term.