Factorize the given expression: \(a^4 - 16\)
Answer
Step 3: Factorize further. Note that \(a^2 - 4\) is also a difference of squares, we can factorize it further into \((a - 2)(a + 2)\). Therefore, the expression \(a^4 - 16\) can be factorized into \((a - 2)(a + 2)(a^2 + 4)\)
Step 1 ：Step 1: Recognize the given expression as a difference of squares. The expression \(a^4 - 16\) can be rewritten as \((a^2)^2 - (4)^2\)
Step 2 ：Step 2: Apply the formula for factoring a difference of squares. The formula is \(a^2 - b^2 = (a-b)(a+b)\). Substituting \(a^2 = a^2\) and \(b^2 = 4\) into the formula, we get: \((a^2 - 4)(a^2 + 4)\)
Step 3 ：Step 3: Factorize further. Note that \(a^2 - 4\) is also a difference of squares, we can factorize it further into \((a - 2)(a + 2)\). Therefore, the expression \(a^4 - 16\) can be factorized into \((a - 2)(a + 2)(a^2 + 4)\)
