# Express Review Guide: Algebra I by LearningExpress Editors

By LearningExpress Editors

Show evaluate courses: Algebra I is helping scholars collect functional talents with speedy, exact classes. All key issues are coated. Readers will make the most of math suggestions, concepts for fending off universal pitfalls, sidebars of math definitions, and an in depth word list. furthermore, pre and posttests support scholars gauge either their vulnerable components in addition to their development.

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Extra info for Express Review Guide: Algebra I

Sample text

Because they appear so often, it is useful to learn to recognize the first few perfect squares: 02 = 0, 12 = 1, 22 = 4, 32 = 9, 42 = 16, 52 = 25, 62 = 36, 72 = 49, 82 = 64, 92 = 81, 102 = 100, 112 = 121, and 122 = 144. It is even easier to recognize when a variable is a perfect square because the exponent is even. For example, x14 = x7 ⋅ x7 and a8 = a4 ⋅ a4. Example 2y10 ͙64x ෆ Write as a square: Evaluate: 5 ⋅ 8ෆ5 ͙8xy ෆxy 8xy5 You could have also split the radical into parts and evaluated them separately: Example 2y10 ͙64x ෆ Split into perfect squares: ͙64 ෆ⋅ ⋅ x2 ෆ y10 Write as squares: 5 ⋅ y5 ͙8 ෆ ⋅ 8 ⋅ ͙xෆ ⋅ x ⋅ ͙yෆ Evaluate: 8 ⋅ x ⋅ y5 Multiply: 8xy5 INSIDE TRACK IF YOUR RADICAL has a coefficient like 3͙25 ෆ, evaluate the square root before multiplying: 3͙25 ෆ = 3 • 5 = 15.

Both of these solutions are true. The solution set of this equation is all real numbers. An equation that is true for all real numbers is called an identity. Following are several inequalities and their descriptions. Again, look carefully at each solution set. 1), . . } For expression 3, {x| x > 3} means all real numbers x that satisfy x > 3. 39 40 Express Review Guides: ALGEBRA I PRACTICE LAP DIRECTIONS: Use scratch paper to solve the following problems. You can check your answers at the end of this chapter.

Associative For any three numbers For any three numbers a, b, property a, b, and c, the expression and c, the expression a • b • c a + b + c can be interpreted can be interpreted either as either as (a + b) + c or as (a • b) • c or as a • (b • c), and a + (b + c), and these two these two products are equal. sums are equal. The identity For any number a, a + 0 = a. For any number a, a • 1 = a. a. Zero, added to any number, One, multiplied by any number, the leave-it-alone leaves that number alone.