How does this polynomial identity work on numerical relationships?

(y + x) (ax + b)

Let us take 'a' in the place of 'y' so the equation becomes

(y+x) (ax+b)

Step-by-step explanation:

Step 1:

(a + x) (ax + b)

Step 2: Proof

Checking polynomial identity.

(ax+b) (x+a) = FOIL

(ax+b) (x+a)

ax^2+a^2x is the First Term in the FOIL

ax^2 + a^2x + bx + ab

(ax+b) (x+a) + bx+ab is the Second Term in the FOIL

Add both expressions together from First and Second Term

= ax^2 + a^2x + bx + ab

Step 3: Proof

(ax+b) (x+a) = ax^2 + a^2x + bx + ab

Identity is Found.

Trying with numbers now

(ax+b) (x+a) = ax^2 + a^2x + bx + ab

((2*5) + 8) (5+2) = (2*5^2) + (2^2*5) + (8*5) + (2*8)

((10) + 8) (7) = (2*25) + (4*5) + (40) + (16)

(18) (7) = (50) + (20) + (56)

126 = 126