Question

Use the distributive property to simplify the expression 3(a+2b)+4(b+5a)

Answer 1

We have

`3\mleft(a+2b\mright)+4\mleft(b+5a\mright)​`

the distributive property is

`x(y+z)=xy+xz`

so we will expand the polynomials given using the distributive property above

`3\mleft(a+2b\mright)+4\mleft(b+5a\mright)​=3a+6b+4b+20a`

we sum similar terms

`23a+10b`

___________________________________________

we have

`3\mleft(a+2b\mright)+4\mleft(b+5a\mright)​`

in order to simplify the expression, we need to the multiplication 3(a+2b) and 4(b+5a)​ using the distributive property

`3(a+2b)=3a+3(2b)=3a+6b`
`4\mleft(b+5a\mright)=4b+4(5a)=4b+20a`

we sum the results obtained

`3a+6b+4b+20a`

then to simplify we sum the similar terms

`23a+10b`