Step by step solution :Step 1 :Equation at the end of step 1 : ((y2) • (q - 4)) - c • (q - 4) Step 2 :Equation at the end of step 2 : y2 • (q - 4) - c • (q - 4) Step 3 :Pulling out like terms :

3.1 Pull out q-4

After pulling out, we are left with :
(q-4) • ( y2 * 1 +( c * (-1) ))

Trying to factor as a Difference of Squares :

3.2 Factoring: y2-c

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =
 A2 - AB + BA - B2 =
 A2 - AB + AB - B2 =
 A2 - B2

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : y2 is the square of y1 

Check : c1 is not a square !!
Ruling : Binomial can not be factored as the difference of two perfect squares

Final result : (q - 4) • (y2 - c)

4 0

3 years ago

The area of a playground is 216 yd^2. The width of the playground is 6 yd longer than its length. Find the length and width of t

zvonat [6]

Let the length of the playground be x, then the width is 6 + x.

Area = length * width = x * (6 + x) = 6x + x^2 = 216

Solving the quadratic equation x^2 + 6x - 216 = 0, we have x = 12 or -18

i.e length = 12 and width = 6 + 18 = 18

5 0

2 years ago