Question

Write an equivalent expression for 6x+5y+7x

Write an equivalent expression for 4g+2 using the distributive property (An explanation would be lovely as well! (: <3 x )

Answer 1

(a)

Given the expression:
`6x+5y+7x`

to find the equivalent expression:

Like terms states that in algebraic expressions, like terms are terms that contain the same variables raised to the same power.

Here, 6x and 7x are like terms

then:

by combine like terms in the given expressions we get;

`14x+5y`

Therefore, the equivalent expression of
`6x+5y+7x` is
`14x+5y`

(b)

Given the expression: 4g +2

Distributive property states that when a number is multiplied by the sum of two numbers, then the first number can be distributed to both of those numbers and multiplied by each of them separately.

i.e
`a\cdot (b+c) = a\cdot b+a\cdot c`

`4g+2 = 2\cdot 2g + 2 \cdot 1`

by distributive property:

`4g + 2 = 2\cdot (2g+1)`

therefore, the equivalent expression of 4g +2 is, 2(2g+1)