User:Leftunknown/Sum times sum

One variable

$$(x+1)(x+1)=x^2+2x+1$$

$$(x+a)(x+1)=x^2+(a+1)x+a$$

$$(x+a)(x+a)=x^2+2ax+a^2$$

$$(ax+1)(x+1)=ax^2+(a+1)x+1$$

$$(ax+a)(x+1)=ax^2+2ax+a$$

$$(ax+1)(x+a)=ax^2+(a^2+1)x+a$$

$$(ax+a)(x+a)=ax^2+(a^2+a)x+a^2$$

$$(ax+1)(ax+1)=a^2x^2+2ax+1$$

$$(ax+a)(ax+1)=a^2x^2+(a^2+a)x+a$$

$$(ax+a)(ax+a)=a^2x^2+2a^2x+a^2$$

Two variables

$$(x+a)(x+b)=x^2+(a+b)x+ab$$

$$(ax+b)(x+1)=ax^2+(a+b)x+b$$

$$(ax+1)(x+b)=ax^2+(ab+1)x+b$$

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

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

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

$$(ax+b)(ax+1)=a^2x^2+(ab+a)x+b$$

$$(ax+b)(ax+b)=a^2x^2+2abx+b^2$$

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

$$(ax+1)(bx+1)=abx^2+(a+b)x+1$$

$$(ax+a)(bx+1)=abx^2+(ab+a)x+a$$

$$(ax+1)(bx+a)=abx^2+(a^2+b)x+a$$

$$(ax+a)(bx+a)=abx^2+(a^2+ab)x+a^2$$

$$(ax+b)(bx+1)=abx^2+(a+b^2)x+b$$

$$(ax+1)(bx+b)=abx^2+(ab+b)x+b$$

$$(ax+b)(bx+b)=abx^2+(ab+b^2)x+b^2$$

$$(ax+a)(bx+b)=abx^2+2abx+ab$$

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