1.
9x + 24y
Correct Answer
A. 3(3x + 8y)
Explanation
The given expression 9x + 24y is equivalent to the expression 3(3x + 8y) because when we distribute the 3 to both terms inside the parentheses, we get 3 multiplied by 3x which is 9x, and 3 multiplied by 8y which is 24y. Therefore, the two expressions are equal. The answer 3(3x + 8y) is the correct one.
2.
7(y + 1) - x(y + 1)
Correct Answer
C. (y + 1)(7 - x)
Explanation
The given expression can be simplified by distributing the terms. First, distribute 7 to both y and 1, which gives 7y + 7. Then, distribute -x to both y and 1, which gives -xy - x. Combining these terms, we get 7y + 7 - xy - x. This matches the expression (y + 1)(7 - x), so the answer is (y + 1)(7 - x).
3.
5(x + 2) + y(x + 2)
Correct Answer
A. (x + 2)(5 + y)
Explanation
The given expression can be simplified by distributing the terms inside the parentheses. By doing so, we get 5x + 10 + xy + 2y. This matches the expression (x + 2)(5 + y), so it is the correct answer.
4.
20x - 10
Correct Answer
A. 10(2x - 1)
Explanation
The given expression 20x - 10 can be factored out as 10(2x - 1). This is the correct answer because when we distribute 10 to the terms inside the parentheses, we get 20x - 10, which matches the original expression.
5.
12mn + 18mp
Correct Answer
A. 6m(2n + 3p)
Explanation
The given expression, 12mn + 18mp, can be factored out by taking out the common factors of 6m. This results in 6m(2n + 3p).
6.
X(x - 1) + 5(x - 1)
Correct Answer
C. (x - 1)(x + 5)
Explanation
The given expression can be simplified by factoring out the common factor of (x - 1) from both terms. This results in (x - 1) multiplied by (x + 5), which is the correct answer.
7.
6a - 4b + 8c
Correct Answer
A. 2(3a - 2b + 4c)
Explanation
The given expression 6a - 4b + 8c can be simplified by factoring out the common terms from each term. The expression 2(3a - 2b + 4c) is the correct answer because it represents the simplified form of the given expression. By distributing the 2 to each term inside the parentheses, we get 6a - 4b + 8c, which matches the original expression.
8.
18x - 12y - 30z
Correct Answer
A. 6x(3x - 2y - 5z)
Explanation
The given expression, 18x - 12y - 30z, can be factored out by finding the greatest common factor (GCF) of the coefficients. The GCF of 18, 12, and 30 is 6. Factoring out 6 from each term gives us 6x(3x - 2y - 5z). Therefore, the correct answer is 6x(3x - 2y - 5z).
9.
Factorize: x²+4x
Correct Answer
A. X(x+4)
Explanation
The given expression can be factorized as x(x+4). This is because we can factor out the common factor of x from both terms, leaving us with x multiplied by (x+4).
10.
Factorize: 10xy - 25yz
Correct Answer
C. 5y(2x - 5z)
Explanation
The given expression, 10xy - 25yz, can be factorized as 5y(2x - 5z). This is because both terms in the expression have a common factor of 5y, which can be factored out. The remaining terms, 2x - 5z, cannot be further simplified or factored. Therefore, the correct factorization is 5y(2x - 5z).