Algebra 1b: Unit 11 Obj 4: Quiz

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Quizzes Created: 14 | Total Attempts: 2,443

Questions: 10 | Attempts: 100 | Updated: Mar 21, 2023

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This Algebra 1B Unit 11 objective 4 quiz focuses on factoring differences of squares. Students will factor expressions such as x2 - 81 into (x-9)(x+9) and similar problems, enhancing their understanding of algebraic techniques and preparing them for advanced mathematical concepts.

Questions and Answers

1.

Factor each difference of squares. x²- 81no spaces in answer

Explanation
The given expression can be factored using the difference of squares formula, which states that a^2 - b^2 = (a + b)(a - b). In this case, a = x and b = 9. Therefore, the expression x^2 - 81 can be factored as (x + 9)(x - 9) or (x - 9)(x + 9).

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2.

Factor each difference of squares. x²- 25no spaces in answer

Explanation
The given expression, x^2 - 25, can be factored using the difference of squares formula. This formula states that a^2 - b^2 can be factored as (a + b)(a - b). In this case, a = x and b = 5. Therefore, the expression can be factored as (x + 5)(x - 5). Additionally, since multiplication is commutative, the order of the factors can be reversed, resulting in (x - 5)(x + 5).

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3.

Factor each difference of squares. x²- 121no spaces in answer

Explanation
The given expression is a difference of squares, where x^2 is the square of x and 121 is the square of 11. When factoring a difference of squares, we use the formula (a^2 - b^2) = (a + b)(a - b). In this case, x^2 - 121 can be factored as (x + 11)(x - 11) or (x - 11)(x + 11).

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4.

Factor each difference of squares. 4x²- 25no spaces in answer

Explanation
The given expression, 4x^2 - 25, can be factored using the difference of squares formula. The formula states that a^2 - b^2 can be factored as (a + b)(a - b). In this case, a is 2x and b is 5. Therefore, the expression can be factored as (2x + 5)(2x - 5) or (2x - 5)(2x + 5).

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5.

Factor each difference of squares. 9x²- 16no spaces in answer

Explanation
The given expression can be factored using the difference of squares formula, which states that a^2 - b^2 = (a+b)(a-b). In this case, a = 3x and b = 4. Therefore, the expression can be factored as (3x+4)(3x-4) or (3x-4)(3x+4).

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