the width of a calculator can be represented by (3x+1) inches. the length of the calculator is twice the width. write a polynomial that represents the area of the calculator.
answer
To find the area of the calculator, we need to multiply the width by the length. Given that the length is twice the width, we can express the length as 2(3x + 1).
Therefore, the polynomial that represents the area A of the calculator is:
A = (3x + 1) * 2(3x + 1)
Expanding this expression, we get:
A = 6x(3x + 1) + 2(3x + 1)
Simplifying further, we have:
A = 18x^2 + 6x + 6x + 2
Finally, combining like terms, we get the polynomial:
A = 18x^2 + 12x + 2
Hence, the polynomial representing the area of the calculator is 18x^2 + 12x + 2.
To find the area of the calculator, we need to multiply the width by the length. Since the length is twice the width, we can express it as 2(3x + 1).
The polynomial representing the area (A) of the calculator can be found by multiplying the width (W = 3x + 1) by the length (L = 2(3x + 1)):
A = W * L
= (3x + 1) * (2(3x + 1))
To simplify this expression, we distribute the 2 to both terms inside the parentheses:
A = (3x + 1)(6x + 2)
Now, we can use the distributive property to expand this expression:
A = 3x * 6x + 3x * 2 + 1 * 6x + 1 * 2
= 18x^2 + 6x + 6x + 2
= 18x^2 + 12x + 2
Therefore, the polynomial that represents the area of the calculator is 18x^2 + 12x + 2.
So if the width = 3x+1
what is twice that ?
recall that area = length x width, so .....