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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

Respuesta :

xKelvin

Answer:

C

Step-by-step explanation:

So we have the expression:

[tex](x+y+3)\times(y+1)[/tex]

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

[tex]=x(y+1)+y(y+1)+3(y+1)[/tex]

Distribute the variables:

[tex]=(xy+x)+(y^2+y)+(3y+3)[/tex]

Rearrange them to combine like terms:

[tex]=y^2+xy+y+3y+x+3\\=y^2+xy+4y+x+3[/tex]

The correct answer is C.

Edit: Typo

WojtekR

[tex](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}[/tex]

Answer C.

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