Answer:
The correct answer is B :)
Step-by-step explanation:
The difference in the area of shape A and shape B is option B which is [tex]12x^{4}+12x^{3}+26x^{2} +8x+12[/tex].
Area of rectangle and square is the extent of surface rectangle and square exhibits into them. The area of rectangle is length * breadth and the area of square is side*side.
We have been given the length of shape A=[tex]7x^{2} +4x+8[/tex] and breadth be [tex]3x^{2} +2[/tex] and the side of shape B be [tex]3x^{2} +2[/tex].
Shape A looks like rectangle and shape B looks like square.
So the area becomes:
Area of shape A =[tex](3x^{2} +2) ( 7x^{2} +4x+8)[/tex]
we have to multiply both expressions
=[tex]21x^{4} +12x^{3} +24x^{2} +14x^{2} +8x+16[/tex]
=[tex]21x^{4} +12x^{3} +38x^{2}+8x+16[/tex]
Area of shape B=[tex](3x^{2} +2)(3x^{2} +2)[/tex]
=[tex]9x^{4} +6x^{2} +6x^{2} +4[/tex]
=[tex]9x^{4} +12x^{2} +4[/tex]
Difference=[tex]21x^{4}+12x^{3}+38x^{2} +8x+16-9x^{4} -12x^{2} -4[/tex]
=[tex]12x^{4} +12x^{3}+26x^{2} +8x+12[/tex]
Hence the difference between shape A and shape B is [tex]12x^{4} +12x^{3}+26x^{2} +8x+12[/tex].
Learn more about area at https://brainly.com/question/25965491
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