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(5y + 3x)(8y - 1)

First, change the subtraction symbol to the addition symbol:

(5y + 3x)(8y + -1)

All together: 40y^{2} + 24xy + -5y + -3x

There are no like terms to combine, so we are done.

FOIL

First: 5y × 8y = 40y^{2}

Outer: 5y(-1) = -5y

Inner: 3x × 8y = 24xy

Last: 3x(-1) = -3x

All together:

40y^{2} + 24xy + -5y + -3x

Again, no like terms, so we are done!

Box Method

First, change subtraction symbol to addition:

Combine like terms:

First:

Outer:

Inner:

Last:

There is no subtraction, so we don't need to worry about adding the opposite.

Combine like term:

49x^{4} + 42x^{2 }+ 9

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