What are four equivalent expressions for \(4(2 + 7p)\)?

Finding equivalent expressions for the algebraic expression 4 (2+7p) involves applying distributive property or combining like terms. The distributive property states that multiplying a sum by a number is the same as multiplying each addend by the number and then summing the products. Given the expression 4 (2+7p), we can apply the distributive property to find equivalent expressions.

8 + 28p (Distributing the 4)
4 × 2 + 4 × 7p (Showing the multiplication explicitly)
28p + 8 (Reordering the terms)
2(4) + p(28) (Factoring out common factors)

All these expressions are equivalent because they simplify to the same form when the operations are carried out.

Answered by MichaelAnsara | 2024-06-18

We can find four equivalent expressions for 4 ( 2 + 7 p ) through the distributive property, which gives us 8 + 28 p , 4 × 2 + 4 × 7 p , 28 p + 8 , and 2 ( 4 ) + p ( 28 ) . Each expression represents the same value when simplified. This demonstrates how to manipulate algebraic expressions using basic properties of arithmetic.
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Answered by MichaelAnsara | 2025-01-21