Answer :
We start with the expression
[tex]$$
3n^2 - 147.
$$[/tex]
Step 1: Factor out the common factor
Both terms in the expression have a factor of [tex]$3$[/tex]. Factoring [tex]$3$[/tex] out gives
[tex]$$
3n^2 - 147 = 3\left(n^2 - 49\right).
$$[/tex]
Step 2: Factor the difference of squares
Notice that the expression inside the parentheses, [tex]$n^2 - 49$[/tex], is a difference of two squares because [tex]$49 = 7^2$[/tex]. Recall that the difference of two squares factors as
[tex]$$
a^2 - b^2 = (a - b)(a + b).
$$[/tex]
Here, [tex]$a=n$[/tex] and [tex]$b=7$[/tex]. Thus,
[tex]$$
n^2 - 49 = (n - 7)(n + 7).
$$[/tex]
Step 3: Write the final factorized form
Substitute the factorization back into the expression:
[tex]$$
3\left(n^2 - 49\right)=3\,(n - 7)(n + 7).
$$[/tex]
Thus, the completely factorized form of the expression is
[tex]$$
3(n - 7)(n + 7).
$$[/tex]
[tex]$$
3n^2 - 147.
$$[/tex]
Step 1: Factor out the common factor
Both terms in the expression have a factor of [tex]$3$[/tex]. Factoring [tex]$3$[/tex] out gives
[tex]$$
3n^2 - 147 = 3\left(n^2 - 49\right).
$$[/tex]
Step 2: Factor the difference of squares
Notice that the expression inside the parentheses, [tex]$n^2 - 49$[/tex], is a difference of two squares because [tex]$49 = 7^2$[/tex]. Recall that the difference of two squares factors as
[tex]$$
a^2 - b^2 = (a - b)(a + b).
$$[/tex]
Here, [tex]$a=n$[/tex] and [tex]$b=7$[/tex]. Thus,
[tex]$$
n^2 - 49 = (n - 7)(n + 7).
$$[/tex]
Step 3: Write the final factorized form
Substitute the factorization back into the expression:
[tex]$$
3\left(n^2 - 49\right)=3\,(n - 7)(n + 7).
$$[/tex]
Thus, the completely factorized form of the expression is
[tex]$$
3(n - 7)(n + 7).
$$[/tex]
