Sure, let's rewrite and simplify the expression [tex]\( 7(10 + 5) \)[/tex] using the Distributive Property of Multiplication over Addition. Here are the steps:
1. Identify the expression to rewrite:
[tex]\( 7(10 + 5) \)[/tex]
2. Apply the Distributive Property:
According to the Distributive Property, [tex]\( a(b + c) = ab + ac \)[/tex]. In this case, [tex]\( a = 7 \)[/tex], [tex]\( b = 10 \)[/tex], and [tex]\( c = 5 \)[/tex].
3. Distribute 7 to both 10 and 5:
[tex]\( 7 \cdot 10 + 7 \cdot 5 \)[/tex]
4. Perform the multiplication:
[tex]\( 7 \cdot 10 = 70 \)[/tex]
[tex]\( 7 \cdot 5 = 35 \)[/tex]
5. Add the results:
[tex]\( 70 + 35 \)[/tex]
6. Simplify:
[tex]\( 70 + 35 = 105 \)[/tex]
So, [tex]\( 7(10 + 5) \)[/tex] using the Distributive Property is rewritten as [tex]\( 7 \cdot 10 + 7 \cdot 5 \)[/tex], and the simplified result is:
[tex]\[ 7(10 + 5) = 105 \][/tex]
