Answer:
[tex]49x^2-7^2=49(x-1)(x+1)[/tex]
Step-by-step explanation:
Factoring
We need to recall this property of binomials:
[tex](a-b)(a+b)= a^2-b^2[/tex]
It allows us to factor the difference between two squares as follows.
[tex]a^2-b^2=(a-b)(a+b)[/tex]
The given expression is
[tex]49x^2-7^2[/tex]
Comparing with the above expression:
[tex]a^2=49x^2[/tex]
Taking square root:
[tex]a = 7x[/tex]
[tex]b^2=7^2[/tex]
Taking square root:
b=7
Factoring:
[tex]49x^2-7^2=(7x-7)(7x+7)[/tex]
Now we can see each factor can be taken out the common factor 7:
[tex]49x^2-7^2=7(x-1)*7(x+1)[/tex]
Multiplying:
[tex]\boxed{49x^2-7^2=49(x-1)(x+1)}[/tex]
