Factoring two algebra two problems.?

(a - 9b)(a + 4b)

(x + 3b)(x + 3b)

1:) a² - 5ab - 36b²

=a² - 9ab + 4ab - 36b² [ because 36 = 6 x 6

= a(a- 9b) + 4b( a - 9b) =2 x3 x 2 x 3

= (a + 4b) ( a - 9b) answer = 4 x 9

=36

also 9 -4 =5 ]

2:) x² + 6xb + 9b²

(x + 3b) ( x+ 3b) [ solve direct because 3 x 3 =9 and 3+3=6]

therefore if the first term is x² only x² then you can solve it directly

a^2 - 5ab - 36b^2 = (a - 9b)(a + 4b)

x^2 + 6xb + 9b^2 = (x + 3b)^2

Your solution is of the form:

(X1a + Y1b) (X2a + Y2b)

You know that :

X1 * X2 = 1 ------> X1 = 1 = X2

Y1 * Y2 = -36

and : (X1*Y2 + Y1*X2) = -5 ------> Y2 + Y1 = -5

So by elimination: your solution is Y1 = -9 and Y2 = 4

Same process for #2:

You get :

X1 = 1 = X2

Y1 = 3 = Y2

Hope it helps!

1) (a+4b)(a-9b)

2) (x+3b)^2

(a-9b)(a+4b)

(x+3b)^2