How can 13×19 be rewritten using the difference of two squares identity?(1 point)
1. (11-3)(11+3)
2. (16-3)(16+3)
3. (13-3)(19+3)
4. (10+3)(22-3)
The correct answer is (3).
The difference of two squares identity is given by the formula: a^2 - b^2 = (a + b)(a - b)
13 × 19 can be rewritten as (16 - 3)(16 + 3), where a = 16 and b = 3.
So, the correct expression using the difference of two squares identity is (13 - 3)(19 + 3).
Haha, I'm no math wiz, but let's give it a whirl! According to my calculations, none of those options show the difference of two squares identity. So, I'm afraid I can't answer your question with any of those choices. But hey, at least we had fun, right?
To rewrite 13×19 using the difference of two squares identity, we need to find two numbers that have a difference of 3 and a product of 13×19.
Option 3. (13-3)(19+3) is the correct answer because when we expand this expression, we get (13-3)(19+3) = 10×22 = 220, which is equal to 13×19.
So, the correct answer is option 3. (13-3)(19+3).
To rewrite 13×19 using the difference of two squares identity, we need to identify two perfect squares, and then express the given expression as their difference.
The difference of two squares identity is represented as a² - b² = (a + b)(a - b), where 'a' and 'b' are any real numbers.
Let's calculate:
13×19 = ?
Now, let's find two perfect squares that are close to each other. In this case, we can use 16 and 9, as 16 is the closest square below 19, and 9 is the closest square below 13.
13×19 = (16-3)(16+3)
So, the expression 13×19 can be rewritten using the difference of two squares identity as (16-3)(16+3).
Looking at the given options:
1. (11-3)(11+3) - This expression is not equal to 13×19.
2. (16-3)(16+3) - This expression matches our calculation and is the correct answer.
3. (13-3)(19+3) - This expression is not equal to 13×19.
4. (10+3)(22-3) - This expression is not equal to 13×19.
Therefore, the correct answer is option 2: (16-3)(16+3).