Precalculus question!!!

Question

Establish the identity.

(a tanθ + b secθ)^2 -(a secθ + b tanθ)^2 = -a^2 + b^2

Square each term on the left side of the identity and simplify by combining like terms. Do not apply any trigonometric identity.

a^2tan^2θ + b^2 sec^2θ - a^2 sec^2θ - b^2 tan^2θ

Factor out -a^2 + b^2 from the expression from the previous step. Enter the factored expression below.

*********I cannot figure out the factored form************

Answer 1

a²tan²θ+2abtanθsecθ+b²sec²θ-a²sec²θ-2absecθtanθ-b²tan²θ

a²tan²θ++b²sec²θ-a²sec²θ-b²tan²θ

(a²-b²)tan²θ+(-a²+b²)sec²θ

-(-a²+b²)tan²θ+(-a²+b²)sec²θ

(-a²+b²)(-tan²θ+sec²θ)

(-a²+b²)(1) Since tan²θ+1=sec²θ

-a²+b²