use the distributive property to remove the parentheses for this question? -5 (4v – 2u – 3)
The Correct Answer and Explanation is:
Correct Answer:
−5(4v−2u−3)=−20v+10u+15-5 (4v – 2u – 3) = -20v + 10u + 15−5(4v−2u−3)=−20v+10u+15
Explanation:
The distributive property is a basic algebraic principle used to eliminate parentheses by multiplying the term outside the parentheses by each term inside the parentheses. The expression presented is:−5(4v−2u−3)-5(4v – 2u – 3)−5(4v−2u−3)
To simplify, multiply −5-5−5 by each term inside the parentheses:
- First, multiply −5-5−5 by 4v4v4v: −5×4v=−20v-5 \times 4v = -20v−5×4v=−20v
- Next, multiply −5-5−5 by −2u-2u−2u: −5×−2u=+10u-5 \times -2u = +10u−5×−2u=+10u A negative times a negative results in a positive product.
- Then, multiply −5-5−5 by −3-3−3: −5×−3=+15-5 \times -3 = +15−5×−3=+15 Again, multiplying two negative numbers yields a positive result.
Now combine all the products:−20v+10u+15-20v + 10u + 15−20v+10u+15
The expression no longer contains parentheses and has been fully simplified using the distributive property.
This property is crucial in algebra because it helps in rewriting expressions in a simpler or more useful form, especially when solving equations or combining like terms. The negative sign outside the parentheses plays a vital role in determining the signs of the resulting terms. If ignored, it could lead to an incorrect answer. Each multiplication step maintains the integrity of the original expression while enabling easier handling in subsequent operations.
Thus, the correct simplified expression is:−20v+10u+15-20v + 10u + 15−20v+10u+15
