Difference of Perfect Squares

Front

What is the difference of perfect squares?

Back

The difference of perfect squares is a mathematical expression that can be factored into the form (a + b)(a - b), where a² - b² = (a + b)(a - b).

Front

What is a perfect square?

Back

A perfect square is a number that can be expressed as the square of an integer. For example, 1, 4, 9, 16, and 25 are perfect squares.

Front

Can we factor using the difference of two squares if there is an addition sign?

Back

No, we cannot factor using the difference of two squares if there is an addition sign; it only applies to subtraction.

Front

Factor the expression: 4x² - 25

Back

(2x + 5)(2x - 5)

Front

Factor the expression: x² - 25

Back

(x + 5)(x - 5)

Front

Factor the expression: x⁴ - 100y²

Back

(x² + 10y)(x² - 10y)

Front

What is the exponent of a perfect square?

Back

The exponent of a perfect square is always even.

Front

Is 49 a perfect square?

Back

Yes, 49 is a perfect square because it can be expressed as 7².

Front

Is 4 a perfect square?

Back

Yes, 4 is a perfect square because it can be expressed as 2².

Front

What is the formula for factoring the difference of squares?

Back

The formula is a² - b² = (a + b)(a - b).