Answer:
[tex]3x^{2} +2x-7[/tex]
Step-by-step explanation:
Given :
Perimeter of a bigger rectangle is represented by [tex]4x^{2} +5x-2[/tex]
Perimeter of a smaller rectangle is represented by [tex]x^{2} +3x+5[/tex]
To Find : Polynomial expression that represents how much larger the first rectangle is than the smaller rectangle.
Solution :
Subtract the equation of perimeter of smaller rectangle from equation of perimeter of a bigger rectangle :
⇒ [tex]4x^{2} +5x-2 - (x^{2} +3x+5)[/tex]
⇒[tex]4x^{2} +5x-2-x^{2} -3x-5[/tex]
⇒[tex]3x^{2} +2x-7[/tex]
So, Polynomial expression that represents how much larger the first rectangle is than the smaller rectangle is [tex]3x^{2} +2x-7[/tex].
Answer:
A) [tex]3x^{2} +2x-7[/tex]
Step-by-step explanation:
You need to subtract the perimeter of the smaller rectangle from the perimeter of the larger rectangle.
[tex](4x^{2} +5x-2) - (x^{2} + 3x +5)[/tex]
Distribute -1 (-) to each [tex](x^{2} + 3x +5)[/tex] :
[tex]4x^{2} +5x-2-x^{2} -3x-5[/tex]
Add like terms & solve:
[tex]3x^{2} +2x-7[/tex]
