Answer:
The expression of the area of rectangle ABCD as simplified polynomial will be:
[tex]A=16x^2-8x[/tex]
Hence, the 2nd option is correct.
Step-by-step explanation:
As we know that the area of a rectangle can be obtained by multiplying the length by the width.
i.e.
[tex]A=l\times w[/tex]
Given
The length of a rectangle ABCD = [tex]l[/tex] = [tex](x+5) + (3x) + (4x-9)[/tex]
The width of a rectangle = [tex]w[/tex] = [tex]2x[/tex]
so the expression of the area of rectangle ABCD as simplified polynomial will be:
[tex]A=l\times w[/tex]
[tex]A=\left[\left(x+5\right)\:+\:\left(3x\right)\:+\:\left(4x-9\right)\right]\:\times \left[2x\right][/tex]
[tex]=\left(\left(x+5\right)+\left(3x\right)+\left(4x-9\right)\right)\left(2x\right)[/tex]
[tex]=\left(x+5+3x+4x-9\right)\times \:2x[/tex]
[tex]=2x\left(8x-4\right)[/tex]
[tex]=16x^2-8x[/tex]
Therefore, the expression of the area of rectangle ABCD as simplified polynomial will be:
[tex]A=16x^2-8x[/tex]
Hence, the 2nd option is correct.
