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Any expression in the format (a2 - b2) is referred to as a "difference of squares". It can always be broken down into the format (√a + √b)(√a - √b).
In this case then, the square root of x2 is equal to x, and the square root of 9 is equal to three. We know then that:
x2 - 9 = (x + 3)(x - 3)
Factor x4 - 81. Step 1: both numbers have square roots and have a minus sign between them so the first factor result is (x2+9)(x2-9). Step 2: (x2+9) does not factor, but (x2-9) factors to (x+3)(x-3). Step 3: Solution is (x2+9)(x+3)(x-3).
x2-6x+9 = (x-3)(x-3) when factorised.
9 - x2 = 32 - x2 = (3 - x)(3 + x)
x2 + 9 + 20 = x2 + 29, and can not be factored.I assume though that you mis-wrote your question, and what you in fact want to ask is how to factor x2 + 9x + 20.In that case, the answer is (x + 4)(x + 5).
x2 + 9 = (x + 3i)(x - 3i) The answer is based on a knowledge of imaginary and complex numbers where i2 = -1