Question

Please help! Explain how to recognize a difference of two squares.

Answer 1

Step-by-step explanation:

(a+b)(a-b)

use a and b in the first bracket to multiply the next bracket ; a(a-b)+b(a-b)

a square-ab+ab-bsquare

Answer 2

Answer:

WHEN THE SUM of two numbers multiplies their difference --

(a + b)(a − b)

-- then the product is the difference of their squares:

(a + b)(a − b) = a2 − b2

For, the like terms will cancel.

Symmetrically, the difference of two squares can be factored:

x2 − 25 = (x + 5)(x − 5)

x2 is the square of x. 25 is the square of 5.

The sum of two squares -- a2 + b2 -- cannot be factored. See Section 2.

Example 1. Multiply (x3 + 2)(x3 − 2).

Solution. Recognize the form:

(a + b)(a − b)

The product will be the difference of two squares:

(x3 + 2)(x3 − 2) = x6 − 4.

x6 is the square of x3. 4 is the square of 2.

Upon seeing the form (a + b)(a − b), the student should not do the FOIL method. The student should recognize immediately that the product will be a2 − b2.

That is skill in algebra.

And the order of factors never matters:

(a + b)(a − b) = (a − b)(a + b) = a2 − b2.