Answer :
To factor the expression [tex]\( 169 - y^6 \)[/tex], we can use the concept of the difference of squares. The difference of squares formula is given by:
[tex]\[ a^2 - b^2 = (a - b)(a + b) \][/tex]
In the expression [tex]\( 169 - y^6 \)[/tex], we can write 169 as [tex]\( 13^2 \)[/tex] and [tex]\( y^6 \)[/tex] as [tex]\( (y^3)^2 \)[/tex]. This gives us the expression in a form that matches the difference of squares:
[tex]\[ 169 - y^6 = 13^2 - (y^3)^2 \][/tex]
Now, we use the difference of squares formula:
1. Identify [tex]\( a = 13 \)[/tex] and [tex]\( b = y^3 \)[/tex]
2. Apply the formula:
[tex]\[ 13^2 - (y^3)^2 = (13 - y^3)(13 + y^3) \][/tex]
Thus, the factored form of the expression [tex]\( 169 - y^6 \)[/tex] is:
[tex]\[ (13 - y^3)(13 + y^3) \][/tex]
This is the complete factorization of the given expression.
[tex]\[ a^2 - b^2 = (a - b)(a + b) \][/tex]
In the expression [tex]\( 169 - y^6 \)[/tex], we can write 169 as [tex]\( 13^2 \)[/tex] and [tex]\( y^6 \)[/tex] as [tex]\( (y^3)^2 \)[/tex]. This gives us the expression in a form that matches the difference of squares:
[tex]\[ 169 - y^6 = 13^2 - (y^3)^2 \][/tex]
Now, we use the difference of squares formula:
1. Identify [tex]\( a = 13 \)[/tex] and [tex]\( b = y^3 \)[/tex]
2. Apply the formula:
[tex]\[ 13^2 - (y^3)^2 = (13 - y^3)(13 + y^3) \][/tex]
Thus, the factored form of the expression [tex]\( 169 - y^6 \)[/tex] is:
[tex]\[ (13 - y^3)(13 + y^3) \][/tex]
This is the complete factorization of the given expression.
