[tex]16yx^{2} -x^{2}[/tex] shows the difference between two squares
Further Explanation
Quadratic identity
- An identity is an equation or an expression that is always true for any value. These equations are true no matter the value plugged in for the variable.
In quadratic expression we have quadratic identities which includes;
1. [tex](a-b)^{2} = a^{2} - 2ab + b^{2}[/tex]
2. [tex](a+b)^{2} = a^{2} + 2ab + b^{2}[/tex]
3. [tex]a^{2} -b^{2} =(a-b)(a+b)[/tex]
Considering the quadratic identity
[tex]a^{2} -b^{2}[/tex]
Which shows the difference between [tex]a^{2}[/tex] and [tex]b^{2}[/tex]
We can expand to show the difference between two squares;
[tex]a^{2} -b^{2}[/tex] may be expanded to [tex](a-b)(a+b)[/tex]
Therefore:
[tex]a^{2} -b^{2}[/tex] is an expression known as difference between two squares, and
[tex](a-b)[/tex] and [tex](a+b)[/tex] are the factors of [tex]a^{2} -b^{2}[/tex]
Proof of the quadratic identity
[tex](a-b)(a+b)[/tex]
Using distributive property we get;
[tex]a^{2} +ab-ab-b^{2}[/tex]
but; [tex]ab-ab=0[/tex]
Therefore;
[tex]a^{2} -b^{2} =(a-b)(a+b)[/tex]
Conclusion
Difference of two perfect squares = sum of two numbers x Difference of two numbers
That is; [tex]a^{2} -b^{2} =(a-b)(a+b)[/tex]
Considering;
[tex]16y^{2} -x^{2}[/tex] is in the form of [tex]a^{2} -b^{2}[/tex]
Its factors will be
[tex]4y-x[/tex] and [tex]4y-x[/tex]
Keywords: Quadratic dentity, difference between squares
Learn more about:
- Difference between two squares: https://brainly.com/question/12462696
- Example and explanation: https://brainly.com/question/12462696
Level: High school
Subject: Mathematics
Topic: Quadratic expressions
Sub-topic: Quadratic identities
