Answer :
To factor the expression [tex]\(16x^2 - 169y^2\)[/tex], we will use the difference of squares method. The difference of squares formula is given by:
[tex]\[ a^2 - b^2 = (a - b)(a + b) \][/tex]
First, let's identify [tex]\(a^2\)[/tex] and [tex]\(b^2\)[/tex] in the expression [tex]\(16x^2 - 169y^2\)[/tex]:
1. [tex]\(16x^2\)[/tex] can be written as [tex]\((4x)^2\)[/tex].
2. [tex]\(169y^2\)[/tex] can be written as [tex]\((13y)^2\)[/tex].
Now, inside the expression [tex]\(16x^2 - 169y^2\)[/tex], we have two perfect squares:
- [tex]\(a = 4x\)[/tex]
- [tex]\(b = 13y\)[/tex]
Now apply the difference of squares formula:
[tex]\[ 16x^2 - 169y^2 = (4x)^2 - (13y)^2 = (4x - 13y)(4x + 13y) \][/tex]
So, the factored form of the expression is:
[tex]\[(4x - 13y)(4x + 13y)\][/tex]
That's the step-by-step solution for factoring the expression [tex]\(16x^2 - 169y^2\)[/tex].
[tex]\[ a^2 - b^2 = (a - b)(a + b) \][/tex]
First, let's identify [tex]\(a^2\)[/tex] and [tex]\(b^2\)[/tex] in the expression [tex]\(16x^2 - 169y^2\)[/tex]:
1. [tex]\(16x^2\)[/tex] can be written as [tex]\((4x)^2\)[/tex].
2. [tex]\(169y^2\)[/tex] can be written as [tex]\((13y)^2\)[/tex].
Now, inside the expression [tex]\(16x^2 - 169y^2\)[/tex], we have two perfect squares:
- [tex]\(a = 4x\)[/tex]
- [tex]\(b = 13y\)[/tex]
Now apply the difference of squares formula:
[tex]\[ 16x^2 - 169y^2 = (4x)^2 - (13y)^2 = (4x - 13y)(4x + 13y) \][/tex]
So, the factored form of the expression is:
[tex]\[(4x - 13y)(4x + 13y)\][/tex]
That's the step-by-step solution for factoring the expression [tex]\(16x^2 - 169y^2\)[/tex].
