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Rauls hamster's house sits in a corner of its cage as shown in the diagram. The area around the house is 5 inches wide. Write an expression, in factored form, that represents the area around the house

Rauls hamsters house sits in a corner of its cage as shown in the diagram The area around the house is 5 inches wide Write an expression in factored form that r class=

Respuesta :

The area around the house can be express is the area of the cage minus the area of the house, that is

[tex]\begin{gathered} A=A_C-A_H \\ =\lbrack(3x+5)(8+5)\rbrack-\lbrack(3x)(8)\rbrack \\ =\lbrack(3x+5)(13)\rbrack-\lbrack24x\rbrack \\ =\lbrack39x+65\rbrack-24x \\ =39x+65-24x \\ =15x+65 \\ =5(3x+13) \end{gathered}[/tex]

Therefore the area around the house is 5(3x+13).

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