Minnie has a piece of cardboard with length (3x^2 − 2x + 1) inches and width (2x^2 + 3x − 4) inches. Which statement best explains why the area of the cardboard demonstrates the closure property?

Question

anonymous · Answer

A) It is equal to (6x^4 + 9x^3 − 12x^2 + 8x − 4) square inches, which is also a polynomial like the length and width.

B) It is equal to (6x^4 + 5x^3 − 16x^2 + 11x − 4) square inches, which is also a polynomial like the length and width.

 C) The length multiplied by the width is equal to the width multiplied by the length.

D) The length multiplied by the width has the same degree as the width multiplied by the length.

anonymous · Answer

can someone please help

hero · Answer

The area of the cardboard can be found by multiplying its length by its width. @mathmorelikeno, Have you tried multiplying $(3x^2 - 2x + 1)(2x^2 + 3x - 4)$ ?

anonymous · Answer

@Hero Yes but I gt 6^4-6x^2-3

anonymous · Answer

got*

hero · Answer

Can you please show the work you did to get that?

anonymous · Answer

(3x^2 − 2x + 1) (2x^2 + 3x − 4)
3 times 2 is six, plus the exponents would be 6x^4. Then I multiplied the second terms which were -2x(3) and got -6x^2 and then -4 plus 1 is -3.

hero · Answer

Actually, it's a bit more multiplication involved than that. What you have to do is use distributive property to multiply:

$(a + b + c)(d + e + f) = a(d + e + f) + b(d + e + f) + c(d + e + f)$

hero · Answer

In this case:
$(3x^2 - 2x + 1)(2x^2 + 3x - 4) = $  
$3x^2(2x^2 + 3x - 4) - 2x(2x^2 + 3x - 4) + 1(2x^2 + 3x - 4)$

anonymous · Answer

Yes thank you so much

hero · Answer

Afterwards expand each term:
 $3x^2(2x^2 + 3x - 4) = 6x^4 + 9x^3 - 12x^2$
$-2x(2x^2 + 3x - 4) = -4x^3 - 6x^2 + 8x$
     $1(2x^2 + 3x - 4) = 2x^2 + 3x - 4$

Finally add each result together:
$(6x^4 + 9x^3 - 12x^2) + (-4x^3 - 6x^2 + 8x) + (2x^2 + 3x - 4)$