select the expression that is equivalent to $a^{2}-144b^{2}$. \n(a) $(a - 12b)^{2}$ \n(b) $(a + 12b)^{2}$…

select the expression that is equivalent to $a^{2}-144b^{2}$. \n(a) $(a - 12b)^{2}$ \n(b) $(a + 12b)^{2}$ \n(c) $(a - 12b)(a + 12b)$ \n(d) $a^{2}-24ab + 144b^{2}$

select the expression that is equivalent to $a^{2}-144b^{2}$. \n(a) $(a - 12b)^{2}$ \n(b) $(a + 12b)^{2}$ \n(c) $(a - 12b)(a + 12b)$ \n(d) $a^{2}-24ab + 144b^{2}$

Answer

Explanation:

Step1: Recall the difference of squares formula

The difference of squares formula is (x^{2}-y^{2}=(x - y)(x + y)). In the expression (a^{2}-144b^{2}), we can rewrite (144b^{2}) as ((12b)^{2}). So, (a^{2}-144b^{2}=a^{2}-(12b)^{2}), where (x = a) and (y=12b).

Step2: Apply the difference of squares formula

Using the formula (x^{2}-y^{2}=(x - y)(x + y)) with (x = a) and (y = 12b), we get (a^{2}-(12b)^{2}=(a - 12b)(a + 12b)).

Let's check the other options:

  • Option A: ((a-12b)^{2}=a^{2}-24ab + 144b^{2}\neq a^{2}-144b^{2}) (using the formula ((m - n)^{2}=m^{2}-2mn + n^{2}) with (m=a) and (n = 12b)).
  • Option B: ((a + 12b)^{2}=a^{2}+24ab+144b^{2}\neq a^{2}-144b^{2}) (using the formula ((m + n)^{2}=m^{2}+2mn + n^{2}) with (m=a) and (n = 12b)).
  • Option D: (a^{2}-24ab + 144b^{2}=(a - 12b)^{2}\neq a^{2}-144b^{2}).

Answer:

C. ((a - 12b)(a + 12b))