Use the distributive property to write an equivalent expression.
10(m + 4n)
The correct answer and explanation is:
To use the distributive property on the expression 10(m+4n)10(m + 4n), the goal is to multiply each term inside the parentheses by the factor outside the parentheses, which in this case is 1010.
The distributive property states that for any numbers aa, bb, and cc, the expression a(b+c)a(b + c) is equivalent to ab+acab + ac.
Here, the expression is 10(m+4n)10(m + 4n). To apply the distributive property, multiply 1010 by both mm and 4n4n: 10(m+4n)=10×m+10×4n10(m + 4n) = 10 \times m + 10 \times 4n
Now simplify: 10×m=10m10 \times m = 10m 10×4n=40n10 \times 4n = 40n
Thus, the equivalent expression is: 10m+40n10m + 40n
Explanation:
The distributive property helps to simplify expressions by eliminating parentheses. By multiplying the term outside the parentheses by each term inside the parentheses, you expand the expression and make it easier to work with. In this case, multiplying 1010 by both mm and 4n4n results in two separate terms, 10m10m and 40n40n, which are added together in the final expression.
The distributive property is useful in algebra, especially when dealing with expressions that contain variables or unknowns. It helps break down complex expressions into simpler terms, making them easier to manipulate or solve in equations.