Algebra basics
Distributive property
ALEKS placementTEAS math
Multiply the outside factor by every term inside, sign included.
What this covers
a(b+c)=ab+ac- Attach the sign to the factor before you distribute.
- Multiply the factor by each term, one at a time.
- Multiply the numbers; a variable part such as x rides along unchanged.
- Combine like terms afterward.
Worked example
Worked example
Expand -4(2x - 3).
- −4⋅2x+(−4)(−3)The factor is -4, negative sign included. It multiplies both terms.
- −8x+12-4 times 2x is -8x. Negative times negative is positive: -4 times -3 is 12.
Another worked example
Expand 4(2x + 3).
- 4(2x+3)=4(2x)+4(3)Both terms receive the outside factor.
- 8x+12Multiply each coefficient separately.
A common mistake
A mistake Lemma catches
From −4(2x−3)
−8x−3−8x+12
“The -4 multiplies every term inside the parentheses, not only 2x: -4·(-3) = 12, but the line still has -3.”
Try one
Sample problem
Expand and simplify.
−5(x+7)Practice distribute free
No account, no email. Every line you type is checked by the same computer algebra system as the worked example above.
Where this fits
Before this
After this