Answer:
[tex]Area = 6x^3+-5x^{2} +6x+5[/tex]
Step-by-step explanation:
Given that:
Length of a rectangle = [tex]3x^2-4x+5[/tex]
Width of rectangle = [tex]2x + 1[/tex]
To find:
Simple polynomial expression for finding the area of rectangle.
Solution:
First of all, we should know about the formula for finding the area of rectangle. Then we should know how to multiply two polynomials.
Formula for area of a rectangle in terms of its length and width is:
[tex]Area= Length \times Width[/tex]
Putting the given values:
[tex]Area = (3x^2-4x+5)(2x+1)[/tex]
Here, we can use the distributive property of multiplication for finding the value of the above multiplication expression.
[tex](A+B)\times (C+D) = A\times C + A\times D+ B\times C + B \times D[/tex]
Therefore, the multiplication of above polynomials can be written as:
[tex]Area = (3x^2-4x+5)(2x+1)\\\Rightarrow Area = 3x^2(2x+1)-4x(2x+1)+5(2x+1)\\\Rightarrow Area = 6x^3+3x^{2} -8x^{2} -4x+10x+5\\\Rightarrow Area = 6x^3+-5x^{2} +6x+5[/tex]
Therefore, the answer is:
[tex]Area = 6x^3+-5x^{2} +6x+5[/tex]
