## Algebra Group 9 Exercises:

Finding roots by factoring the difference of two squares

Note: 2@x means x squared. For example, 2@3 = 9.

The fact that the difference of two squares factors (that is, can be written as a non-trivial product) is fundamental to algebra. This fact is like the base of an obelisk: It has a small footprint, but much rests on it.

2@P - 2@Q = (P - Q)(P + Q)

For example, 2@5 - 2@4 = 25 - 16 = 9, and (5 - 4)(5 + 4) = 1x9 = 9.

2@x - 49 = 0 if, and only if, (click here for answer)

2@x - 64 = 0 if, and only if, (click here for answer)

2@x - 81 = 0 if, and only if, (click here for answer)

2@x - 100 = 0 if, and only if, (click here for answer)

2@x - 2@(x - 4) = 0 if, and only if, (click here for answer)

2@x - 2@(x - 10) = 0 if, and only if, (click here for answer)

Go to Algebra Group 10 Exercises

(end of page)

The fact that the difference of two squares factors (that is, can be written as a non-trivial product) is fundamental to algebra. This fact is like the base of an obelisk: It has a small footprint, but much rests on it.

2@P - 2@Q = (P - Q)(P + Q)

For example, 2@5 - 2@4 = 25 - 16 = 9, and (5 - 4)(5 + 4) = 1x9 = 9.

2@x - 49 = 0 if, and only if, (click here for answer)

2@x - 64 = 0 if, and only if, (click here for answer)

2@x - 81 = 0 if, and only if, (click here for answer)

2@x - 100 = 0 if, and only if, (click here for answer)

2@x - 2@(x - 4) = 0 if, and only if, (click here for answer)

2@x - 2@(x - 10) = 0 if, and only if, (click here for answer)

Go to Algebra Group 10 Exercises

(end of page)