Question

Write an equivalent expression by applying the distributive property (x + y + 3) x (y + 1) = A: 2y2+xy+4 B: 2y + x + 4 C: y2+xy+4y+x+3 Please help math makes me go insane

Answer 1

Answer:

C

Step-by-step explanation:

So we have the expression:

$(x+y+3)\times(y+1)$

To multiply, use the distributive property. Multiply (y+1) to each term on the left:

$=x(y+1)+y(y+1)+3(y+1)$

Distribute the variables:

$=(xy+x)+(y^2+y)+(3y+3)$

Rearrange them to combine like terms:

$=y^2+xy+y+3y+x+3\\=y^2+xy+4y+x+3$

The correct answer is C.

Edit: Typo

Answer 2

$(x+y+3)\cdot(y+1)=\\\\=(x+y+3)\cdot y+(x+y+3)\cdot1=\\\\=xy+y^2+3y+x+y+3=\\\\=\boxed{y^2+xy+4y+x+3}$

Answer C.