What are the characteristics of a difference of squares?
A binomial is a Difference of Squares if both terms are perfect squares. Recall we may have to factor out a common factor first. If we determine that a binomial is a difference of squares, we factor it into two binomials. The first being the square root of the first term minus the square root of the second term.
Which polynomial can be simplified to a difference of squares?
Step-by-step explanation: For the polynomial: 16a^2 – 4a + 4a – 1 = 16a^2 – 1 = (4a – 1)(4a + 1). This polynomial simplifies to a difference of two squares.
Which of the following is a difference of perfect squares?
x2 is already written as a perfect square and 36 written as a perfect square is 62….The Difference of Perfect Squares.
| Step 1: Write the equation in the general form ax2 + bx + c = 0. Add 37 to both sides. | 4×2 – 25 = 0 |
|---|---|
| Step 4: Set each factor to zero and solve for x. | (2x + 5) = 0, or (2x – 5) = 0 x = − 5 2 , or x = 5 2 |
How do you factor the sum and difference of two squares?
Find the square roots of the two terms that are perfect squares. Write the factorization as the sum and difference of the square roots. The sum of the roots is 3x + 4 and the difference between the roots is 3x – 4.
Which numbers can be written as the difference of two squares?
Since a – b = 1, b = a-1, so b = \frac{p+1}{2} – 1 = \frac{p-1}{2}. Thus, any odd prime can be written as the difference of two squares. Any square number n can also be written as the difference of two squares, by taking a = \sqrt{n} and b = 0.
How do you know if a polynomial is a difference of squares?
Factoring Polynomials: The difference of two squares
- It must be a binomial (have two terms)
- Both terms must be perfect squares (meaning that you could take the square root and they would come out evenly.)
- There must be a subtraction/negative sign (not addition) in between them.
Which polynomial is a difference of two squares?
x2 – 25
Answer: The polynomial that is the difference of two squares is x2 – 25. Let us see how we will use the concept of factoring polynomials that are used to express the differences between two perfect squares.
How is the difference of two squares expressed?
A difference of square is expressed in the form: a 2 – b 2, where both the first and last term is perfect squares. Factoring the difference of the two squares gives:
How do you factor the difference of squares?
To factor a difference of squares, the following steps are undertaken: Check if the terms have the greatest common factor (GCF) and factor it out. Remember to include the GCF in your final answer. Determine the numbers that will produce the same results and apply the formula: a 2 – b 2 = (a + b) (a – b) or (a – b) (a + b)
Do you add or subtract the difference of two squares?
Since both are squared terms and being separated by subtraction, this is truly a case of difference of two squares. You may keep it in that form as your final answer. But the best answer is to combine like terms by adding or subtracting the constants. This also simplifies the answer by getting rid of the inner parenthesis.
Is the difference of two squares a theorem?
The difference of two squares is a theorem that tells us if a quadratic equation can be written as a product of two binomials, in which one shows the difference of the square roots and the other shows the sum of the square roots. One thing to note about this theorem is that it does not apply to the SUM of squares.