Respuesta :
Answer:
[tex]SA=10x^2+38x+30[/tex]
Step-by-step explanation:
Please consider the complete question.
You are painting the outside of a jewelry box including the bottom. To find the surface area (S.A) of the jewelry box, you can use the formula [tex]SA=2wl+2lh+2wh[/tex], where L is length, W is width, and H is height. What is the surface area of the jewelry box in terms of x."
[tex]L = 2x+5[/tex]
[tex]W= x[/tex]
[tex]H= x+3[/tex]
To find the surface area of box in terms of x, we will substitute the given values of length, width, and height in terms of x as:
[tex]SA=2x(2x+5)+2(2x+5)(x+3)+2x(x+3)[/tex]
Now, we will use distributive property [tex]a(b+c)=ac+ac[/tex] to simplify our expression as:
[tex]SA=4x^2+10x+(4x+10)(x+3)+2x^2+6x[/tex]
[tex]SA=4x^2+10x+4x(x+3)+10(x+3)+2x^2+6x[/tex]
[tex]SA=4x^2+10x+4x^2+12x+10x+30+2x^2+6x[/tex]
Let us combine like terms.
[tex]SA=4x^2+4x^2+2x^2+10x+12x+10x+6x+30[/tex]
[tex]SA=10x^2+38x+30[/tex]
Therefore, the surface area of the jewelry box in terms of x would be [tex]10x^2+38x+30[/tex].
