18. Factor the following difference of squares. $$ 16 x^{2}-y^{2} $$ a $$ (4 x+y)(4 x-y) $$ b $$ (x+4 y)(x-4 y) $$ c $$ (x+y)(4 x-y) $$ d $$ (4 x-y)(4 x-y) $$

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The correct answer is a. $$ (4x + y)(4x - y) $$. To factor the expression $$ 16x^2 - y^2 $$, we recognize that it is a difference of squares. The general formula for factoring a difference of squares is: $$ a^2 - b^2 = (a - b)(a + b) $$ In this case, we can identify: - $$ a^2 = 16x^2 $$ which means $$ a = 4x $$ - $$ b^2 = y^2 $$ which means $$ b = y $$ Now we can apply the difference of squares formula: $$ 16x^2 - y^2 = (4x - y)(4x + y) $$ Looking at the answer choices provided: a) $$ (4x + y)(4x - y) $$ b) $$ (x + 4y)(x - 4y) $$ c) $$ (x + y)(4x - y) $$ d) $$ (4x - y)(4x - y) $$ The correct factorization is: **a) $$ (4x + y)(4x - y) $$** So the answer is **a**.

18. Factor the following difference of squares. \( 16 x^{2}-y^{2} \) a \( (4 x+y)(4 x-y) \) b \( (x+4 y)(x-4 y) \) c \( (x+y)(4 x-y) \) d \( (4 x-y)(4 x-y) \)

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18. Factor the following difference of squares. \( 16 x^{2}-y^{2} \) a \( (4 x+y)(4 x-y) \) b \( (x+4 y)(x-4 y) \) c \( (x+y)(4 x-y) \) d \( (4 x-y)(4 x-y) \)

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