Question

Find the square of numbers or the product of the numbers using one or more of these identities.

a) (a - b)² = a² - 2ab + b²
b) (a + b)² = a² + 2ab + b²
c) a² - b² = (a + b)(a - b)
d) √(a²b²) = ab

Answer 1

In algebra, finding the square of a number and using identities such as (a + b)² simplifies expressions and aids in solving equations. The Pythagorean theorem is an application where one 'undoes' a square by taking the square root to find a side length of a right triangle.

Step-by-step explanation:

To find the square of a number means to multiply that number by itself, which can be expressed using exponents. For instance, taking 5 squared (5²), we calculate 5 x 5, which equals 25. When dealing with identities in algebra, we use specific formulas to simplify expressions or solve equations more efficiently.

For example, the identity (a + b)² = a² + 2ab + b² helps to expand a binomial that is squared without manually performing the multiplication. Similarly, the identity a² - b² = (a + b)(a - b) allows us to factor a difference of squares into a product of binomials, which is especially useful in solving equations. To 'undo' a square, such as finding the side length a in the Pythagorean theorem a² + b² = c², we would take the square root of both sides after isolating a².