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How to write an expression for the area of a rectangle. Length =x^2-4x+5. Width =x+8. Please explainnnnn.
Algebra 1



Answer :

Answer:

The area = x³ + 4x² - 27x + 40

Step-by-step explanation:

We can find the expression for the area of the rectangle by using the distributive property formula:

[tex]\boxed{a(b+c)=ab+ac}[/tex]

[tex]Area=length\times width[/tex]

[tex]Area=(x^2-4x+5)(x+8)[/tex]

Let:

  • [tex](x^2-4x+5)=a[/tex]
  • [tex](x+8)=(b+c)[/tex]

Then:

[tex]Area=(x^2-4x+5)(x+8)[/tex]

        [tex]=(x^2-4x+5)(x)+(x^2-4x+5)(8)[/tex]

        [tex]=(x^3-4x^2+5x)+(8x^2-32x+40)[/tex]

        [tex]=x^3-4x^2+8x^2+5x-32x+40[/tex]

        [tex]=x^3+4x^2-27x+40[/tex]

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