Factoring two more equations
49x^2-100z^2
32t^2-50
I'll give you a few hints.
What number squared equals 49?
What number squared equals 100?
(?x + ?z)(?x - ?z)
Fill in the question marks and you should have your factors.
Factor out 2 on the second one to start. You should be able to take it from there. (It's similar to your first problem.)
I hope this will help get you started.
Sure! Let's factor the given equations step by step.
1. Factoring 49x^2 - 100z^2:
First, let's identify the perfect squares in the equation.
49 is a perfect square because the square root of 49 is 7.
100 is also a perfect square because the square root of 100 is 10.
Now, we can write the equation as:
49x^2 - 100z^2 = (7x)^2 - (10z)^2
To factor this expression, we can use the difference of squares formula. The difference of squares formula states that:
a^2 - b^2 = (a + b)(a - b)
Using this formula, we can factor our expression as:
(7x + 10z)(7x - 10z)
So, the factored form of 49x^2 - 100z^2 is (7x + 10z)(7x - 10z).
2. Factoring 32t^2 - 50:
First, let's factor out 2 from the equation so that we have a common factor:
32t^2 - 50 = 2(16t^2 - 25)
Now, let's focus on factoring the expression within the parentheses (16t^2 - 25).
Again, let's identify the perfect squares in this equation.
16 is a perfect square because the square root of 16 is 4.
25 is also a perfect square because the square root of 25 is 5.
Now, we can write the expression as:
16t^2 - 25 = (4t)^2 - 5^2
Similar to the first equation, we can use the difference of squares formula to factor the expression:
(4t + 5)(4t - 5)
So, the factored form of 32t^2 - 50 is 2(4t + 5)(4t - 5).
By following these steps, you can factor both equations.