Answer:
Problem: Equivalent expression:
3(3 + x) → 9 + 3x (You can also write it as 3x + 9)
4x - 20 → 4(x - 5)
(9 - 5)x → 9x - 5x
4x + 7x → (4 + 7)x
3(2x + 1) → 6x + 3
10x - 5 → 5(2x - 1)
x + 2x + 3x → x(1 + 2+ 3)
1/2(x - 6) → 1/2x - 3
y(3x + 4z) → 3xy + 4yz
2xyz - 3yz + 4xz → z(2xy - 3y + 4x)
Explanation:
For the expressions labelled under 'Product,' just think of multiplying the variable/number to the rest of the ones within the expression!
So, for example, y(3x + 4z). The parentheses mean multiplication! So we have to multiply 3x and 4z by y.
3x · y = 3xy
4z · y = 4yz
So together as a sum, it would be 3xy + 4yz
For the expressions labelled under sum/difference, just think of something that each one has in common. That is what you'll be multiplying each one with.
For example, 4x + 7x.
What does 4x and 7x have in common with each other? Well, they both have the variable x! So that's what you're going to multiply the parentheses with.
4x + 7x → x(4 + 7)
You can check your answer by distributing the x to the 4 and 7 again.