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

$23a+10b$

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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

$23a+10b$