Shape AShape B3x? + 27x² + 4x + 83x² + 2If shape B is a square, which polynomial represents the difference of the areas of shape A and shape B?CA. 12:04 + 12.13 + 2612 + 81 + 12OB. 32x2 + 8 + 28DC.30.04 + 12 13 + 40.42 + 8 + 20OD8x2 + 8 + 12ResetNextEmentum. All right

Shape AShape B3x 27x 4x 83x 2If shape B is a square which polynomial represents the difference of the areas of shape A and shape BCA 1204 1213 2612 81 12OB 32x2 class=

Respuesta :

ANSWER:

[tex]12x^4+12^3+26x^2+8x+12[/tex]

STEP-BY-STEP EXPLANATION:

We must calculate the area in each case and then do the subtraction, like this:

[tex]\begin{gathered} A=\mleft(3x^2+2\mright)\cdot\mleft(7x^2+4x+8\mright)=21x^4+12x^3+24x^2+14x^2+8x+16=21x^4+12x^3+38x^2+8x+16 \\ B=\mleft(3x^2+2\mright)^2=9x^4+12x^2+4 \end{gathered}[/tex]

The difference would be the following:

[tex]\begin{gathered} A-B=21x^4+12x^3+38x^2+8x+16-9x^4+12x^2+4 \\ A-B=12x^4+12^3+26x^2+8x+12 \end{gathered}[/tex]