Hallo,
4x *(x+7)= 4x *x +4x*7 = 4x^2 +28x
(r+3)*(s+4)= rs +4r+3s +12
(6a+9)*(4b-6)= 6a *4b + -6a*6 +9*4b -9*6= 24ab -36a+36b -54
(3x+y)*(3x+4y)= 9x^2 +12xy +3xy+4y^2 =9x^2 +15xy +4y^2
(m-n)*(m+n)=m^2-n^2
(2a+6b)*(5a+2b+4c) =10a^2 +4ab +8ac +30ab +12b^2 +24bc
=10a^2 +34ab +8ac +12b^2 +24bc
(3x-2y+6z)*(4x-3z) =12x^2 -9xz -8xy+6yz +24xz-18z^2
=12x^2 -8xy+6yz +15xz-18z^2