Answer:
(a + 2b)(a - b)
Step-by-step explanation:
Assuming you require the expression to be factored
Given
a² +
ab - b² ← factor out
from each term
= (a² + ab - 2b²) ← factor the quadratic
Consider the factors of the coefficient of the b² term(- 2) which sum to give the coefficient of the ab- term (+ 1)
The factors are + 2 and - 1, since
2 × - 1 = - 2 and 2 - 1 = + 1, thus
a² + ab - 2b² = (a + 2b)(a - b) and
a² +
ab - b² =
(a + 2b)(a - b)
The perimeter of a rectangle is given by:
In the problem we have these data:
We replace the data in the equation of the perimeter:
<h3>6 + 2 (-2x + 20) = 2 (a - 2x + 20) </h3>
We apply distributive property:
6 - 4x + 40 = 2a - 4x + 40
6 = 2a
6 ÷ 2 = a
3 = a
⇒ Length = 3
The area of the rectangle is given by:
We have these data:
We replace the data in the equation of the area:
<h3>Area = (3) (- 2x + 20) </h3>
We apply the distributive property and obtain:
Area = -6x + 60
<u>The expression representing the area of the rectangle will be -6x + 60</u>
<h3>I hope I've helped!</h3>