you see because 81 is a square #. its all really easy.
so if you want to check it you do this:
(x+9)(x-9)
you multiple the two x's to get x^2.
then you 9 times x to get 9x and you also do -9 times x to get -9x. and -9x+9x cancel out. then you do -9times 9 and get -81. so you end up with x^2-81
Answers & Comments
Verified answer
same as x^2 + 9x - 9x - 81
(x + 9) (x - 9)
Notice that both terms are perfect squares.
x² = x * x = (x)²
81 = 9 * 9 = (9)²
x² - 81 = (x)² - (9)²
Remember how to factor the difference of two perfect squares:
(a - b)(a + b) = a² - b²
Given: x² - 81 = (x)² - (9)²
Means: a = x, b = 9
Apply what you know.
x² - 81 = (x)² - (9)² = (x - 9)(x + 9)
(x+9)(x-9)
you see because 81 is a square #. its all really easy.
so if you want to check it you do this:
(x+9)(x-9)
you multiple the two x's to get x^2.
then you 9 times x to get 9x and you also do -9 times x to get -9x. and -9x+9x cancel out. then you do -9times 9 and get -81. so you end up with x^2-81
a^2 - b^2 = (a+b)*(a-b)
so
x^2 - 81
=> x^2 - 9^2
=> (x+9)*(x-9)
that form is --> a^2 - b^2
for that form, there is simple formula --> (a+b) * (a-b)
so, x^2 - 81
(x + 9) * (x - 9)
( x - 9 ) ( x + 9 )
(x + 9) (x - 9)
(x-9)(x+9)
x^2 + 12x + 5 aspects use the quadratic formulation b^2-4ac one hundred forty four-20 124 +/-sqrt124 relax of q.f. (-b+/-sqrt124)/2a (-12+/-sqrt124)/2 sqrt124= sqrt4sqrt31= 2sqrt31 (-6+/-sqrt31) (x+(6+sqrt31))(x+(6-sqrt31))
(x-3)(X+3)(X+9)