(3x^2-7x-4)-(6x^2-6x+1)
= 3x^2 - 7x - 4 - 6x^2 + 6x - 1 (distribute negative sign)
= -3x^2 -x - 5 (combine like terms)
Write the perimeter of the figure as a polynomial. Simplify. A trapezoid is shown. The top side is labeled 2 x. The right side is labeled 4 x plus 1. The bottom side is labeled 3 x. The left side is labeled 4 x plus 1.
The perimeter of the trapezoid is the sum of all four sides.
2x + (4x + 1) + 3x + (4x + 1)
= 13x + 2
Thus, the polynomial representing the perimeter of the trapezoid is 13x + 2.
To subtract the expression (3x^2 - 7x - 4) from (6x^2 - 6x + 1), we can start by distributing the negative sign to each term inside the second parentheses:
(6x^2 - 6x + 1) becomes (-6x^2 + 6x - 1)
Now, we can combine like terms by adding or subtracting the corresponding coefficients:
(3x^2 - 6x^2) + (-7x + 6x) + (-4 - 1)
First, subtract the coefficients of the x^2 terms:
3x^2 - 6x^2 = -3x^2
Then, combine the coefficients of the x terms:
-7x + 6x = -x
Finally, combine the constant terms:
-4 - 1 = -5
Putting it all together, the expression (3x^2 - 7x - 4) - (6x^2 - 6x + 1) simplifies to:
-3x^2 - x - 5