To determine which of the given expressions are perfect squares, we need to simplify each expression and check if they can be written as the square of a binomial.

(a) 16a^2 + 36b^2 - 48ab:
To check if this expression is a perfect square, we can factor it.
16a^2 + 36b^2 - 48ab = (4a - 6b)^2
Since we can write it as the square of a binomial, expression (a) is a perfect square.

(b) 9x^2 + 18xy + 9y^2:
Similarly, we can factor this expression to check if it is a perfect square.
9x^2 + 18xy + 9y^2 = (3x + 3y)^2
Therefore, expression (b) is also a perfect square.

(c) Both (a) and (b):
Since we have determined that both expression (a) and expression (b) are perfect squares, the correct answer is (c) - Both (a) and (b).

(d) Neither (a) nor (b):
This option is incorrect since we have found that both expression (a) and expression (b) are perfect squares.

Question

To determine which of the given expressions are perfect squares, we need to simplify each expression and check if they can be written as the square of a binomial.

(a) 16a^2 + 36b^2 - 48ab:
To check if this expression is a perfect square, we can factor it. 
16a^2 + 36b^2 - 48ab = (4a - 6b)^2
Since we can write it as the square of a binomial, expression (a) is a perfect square.

(b) 9x^2 + 18xy + 9y^2:
Similarly, we can factor this expression to check if it is a perfect square.
9x^2 + 18xy + 9y^2 = (3x + 3y)^2
Therefore, expression (b) is also a perfect square.

(c) Both (a) and (b):
Since we have determined that both expression (a) and expression (b) are perfect squares, the correct answer is (c) - Both (a) and (b).

(d) Neither (a) nor (b):
This option is incorrect since we have found that both expression (a) and expression (b) are perfect squares.

Knowee AI · Accepted Answer

To determine which of the given expressions are perfect squares, we need to simplify each expression and check if they can be written as the square of a binomial.

(a) 16a^2 + 36b^2 - 48ab:
To check if this expression is a perfect square, we can factor it. 
16a^2 + 36b^2 - 48ab = (4a - 6b)^2
Since we can write it as the square of a binomial, expression (a) is a perfect square.

(b) 9x^2 + 18xy + 9y^2:
Similarly, we can factor this expression to check if it is a perfect square.
9x^2 + 18xy + 9y^2 = (3x + 3y)^2
Therefore, expression (b) is also a perfect square.

(c) Both (a) and (b):
Since we have determined that both expression (a) and expression (b) are perfect squares, the correct answer is (c) - Both (a) and (b).

(d) Neither (a) nor (b):
This option is incorrect since we have found that both expression (a) and expression (b) are perfect squares.

Which of the following is/are perfect squares?(a) 16a2 + 36b2 − 48ab(b) 9x2 + 18xy + 9y2(c) Both (a) and (b)(d) Neither (a) nor (b)

Question

Which of the following is/are perfect squares?

Solution

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