x(x + y) = x^2 + xy multiplying polynomials by monomials?

Question

if x(x + y) = x^2 + xy shouldnt
2x(x + y) = 3x +xy? The answer is 2x^2 + 2xy.

Could someone please spell this out to me? =)

Answer 1

Everything inside the brackets is multiplied by the expression outside the brackets
2x(x+y) = (2x times x ) +( 2x times y)
= 2x*2 + 2xy

Answer 2

When you multiply a polynominal by a monomial, you have to **multiply** the monomial by **each** item in the polynomial. So:

2(x + 4) = (2*x) + (2*4) = 2x + 8
3(x - 5) = (3*x) - (3*5) = 3x - 15
2(a + b + c) = 2a + 2b + 2c

Hope that helps.

Answer 3

It's hard to explain this without visuals. You are using the distributive property when doing this. You distribute the x (you monomial) to each term of the polynomial. (To think of it in silly terms, the bunny on the outside of the fence wants to jump over the fence and hop on each flower.) When you distribute the monomial, you multply the terms together. Hope this makes sense.

Answer 4

you are multiplying not adding, when doing multiplication of monomial times a polynomial you add the exponents of the factors if the bases are the same.and multiply rationals time rational.

Answer 5

x(x+y)=x*x+x*y
x^2+xy distributive property
2x(x+y)=2x^2+2xy again the same rule
2x*x+2x*y
=2x^2+2xy