Mathematics: Algebraic Expressions Flashcards

What is the result of subtracting the expression (2x² - 5xy + 3y²) from (7x² + 2xy - y²)?

Answer: 5x² + 7xy - 4y²

To subtract (2x² - 5xy + 3y²) from (7x² + 2xy - y²), you change the sign of each term in the second expression and add it to the first: (7x² + 2xy - y²) + (-2x² + 5xy - 3y²). Combine like terms: (7x² - 2x²) + (2xy + 5xy) + (-y² - 3y²) = 5x² + 7xy - 4y².

The area of a rectangle is given by the expression (8x² + 10x - 3). If its length is (4x - 1), what is its width?

Answer: 2x + 3

To find the width, you need to find which binomial, when multiplied by the length (4x - 1), gives the area (8x² + 10x - 3). By multiplying the options, we see that (4x - 1)(2x + 3) = 4x(2x) + 4x(3) - 1(2x) - 1(3) = 8x² + 12x - 2x - 3 = 8x² + 10x - 3.

If p = -3, what is the value of the algebraic expression 2p³ - 4p² + 5p?

Answer: -105

Substitute p = -3 into the expression: 2(-3)³ - 4(-3)² + 5(-3). Calculate the powers first: 2(-27) - 4(9) + 5(-3). Then, perform the multiplications: -54 - 36 - 15. Finally, add the numbers: -90 - 15 = -105.

Which of the following is the correct product of the binomials (3a - 5b) and (3a + 5b)?

Answer: 9a² - 25b²

This multiplication follows the special identity (x - y)(x + y) = x² - y². Here, x = 3a and y = 5b. Therefore, the product is (3a)² - (5b)², which simplifies to 9a² - 25b².

What is the sum of the algebraic expressions (4m² - 2mn + 7) and (-3mn + 2n² - 5)?

Answer: 4m² - 5mn + 2n² + 2

To add the expressions, write them out and combine the terms that are alike: 4m² + (-2mn - 3mn) + 2n² + (7 - 5). The m² term (4m²) has no like term. The mn terms combine to -5mn. The n² term (2n²) has no like term. The constant terms combine to +2. The final sum is 4m² - 5mn + 2n² + 2.

An algebraic expression that contains exactly two, unlike terms is called a:

Answer: Binomial

By definition, an algebraic expression with one term is a monomial, two unlike terms is a binomial, and three unlike terms is a trinomial. A polynomial is a general term for an expression with one or more terms.