What is (4x-5y plus 3) (2x plus 7y-7)?

To find the product of the expressions ((4x - 5y + 3)) and ((2x + 7y - 7)), apply the distributive property (also known as the FOIL method for binomials). When multiplied, you get:

[ (4x)(2x) + (4x)(7y) + (4x)(-7) - (5y)(2x) - (5y)(7y) - (5y)(-7) + (3)(2x) + (3)(7y) + (3)(-7) ]

Combining all the terms results in:

[ 8x^2 + 28xy - 28x - 10xy - 35y^2 + 35 + 6x + 21y - 21 ]

Combining like terms yields:

[ 8x^2 + (28xy - 10xy) + (-28x + 6x) + (-35y^2 + 21y) + (35 - 21) ]

The final simplified expression is:

[ 8x^2 + 18xy - 22x - 35y^2 + 14 ]