Use the distributive property to write an equivalent expression.
7(g – 10h + 4)
The correct answer and explanation is:
To apply the distributive property to the expression 7(g−10h+4)7(g – 10h + 4), you distribute the 7 to each term inside the parentheses. The distributive property states that a(b+c+d)=ab+ac+ada(b + c + d) = ab + ac + ad. In this case, the 7 is multiplying each of the three terms inside the parentheses: gg, −10h-10h, and 44.
Start by multiplying each term:
- Multiply 7×g7 \times g, which gives 7g7g.
- Multiply 7×−10h7 \times -10h, which gives −70h-70h.
- Multiply 7×47 \times 4, which gives 2828.
Now, put the terms together to form the equivalent expression: 7g−70h+287g – 70h + 28
Thus, the equivalent expression is 7g−70h+287g – 70h + 28.
The distributive property helps simplify expressions by eliminating parentheses and making it easier to work with algebraic terms. It is a fundamental concept in algebra, allowing for the breakdown of complex expressions into simpler components. By distributing a factor over terms inside parentheses, it ensures that the factor is applied to every individual term, which maintains the overall balance of the expression.
Using the distributive property in this way also prepares expressions for further simplifications, such as combining like terms or solving for unknowns. It is an essential skill in algebra and is used frequently in both basic and advanced problem-solving tasks.