The standard form for a quadratic is
#color(white)("XXX")y=ax^2+bx+c#
(with constants #a, b, c#)
The given form: #y=(5x+2)(6x+8)#
can easily be converted to this standard form by multiplying the factors on the right side.
There are several ways that the multiplication can be done:
Using the Distributive Property
#(5x+2)(6x+8)#
#color(white)("XXX")=5x(6x+8)+2(6x+8)#
#color(white)("XXX")=(30x^2+40x)+(12x+16)#
(then combining like terms:)
#color(white)("XXX")30x^2+52x+16#
#"------------------------------------------------------------------------"#
FOIL
#color(white)("XX"){:
(color(red)("Multiply"),,),
("First terms:", 5x xx 6x, = 30x^2),
("Outside terms:", 5x xx 8, =40x),
("Inside terms:",2 xx 6x, = 12x),
("Last terms:", 2 xx 8, =16),
(color(red)("Add"),,),
(,,color(blue)(30x^2+52x+16))
:}#
#"------------------------------------------------------------------------"#
Tabular Multiplication
#{:
(xx,"|",5x,+2),
("----",,"----","----"),
(6x,"|",color(orange)(30x^2),color(green)(+12x)),
(+8,"|",color(green)(40x),color(cyan)(+16)),
("----","----","----","----"),
(,color(orange)(30x^2),color(green)(+52x),color(cyan)(+16))
:}#
