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Factor the expression:

[tex]169 - y^6[/tex]

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.

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