The equation after filling the blank with the use of an area model to multiply (2x 9)(3x 4). is,
[tex]6x^2+35x+36[/tex]
The area models are help to represent and find the multiplication of binomials in terms of polynomial equation.
The area model is a rectangle shape diagram which is used to solve the problem related to multiply or divide. In this model, factors are specified as the length and width of that rectangle.
The binomial or linear form of equation are given as,
[tex](2x+ 9)\\(3x+ 4)[/tex]
Let multiply of this binomial is f(x). Thus,
[tex]f(x)=(2x+ 9)\times(3x+ 4)[/tex]
Multiply this binomial factors,
[tex]f(x)=(2x+ 9)\times(3x+ 4)\\f(x)=2x(3x+ 4)+9(3x+ 4)\\f(x)=6x^2+8x+27x+36\\f(x)=6x^2+35x+36[/tex]
The figure of the area model of the given problem is attached below.
Hence, the equation after filling the blank with the use of an area model to multiply (4x 3)(2x 5) is,
[tex]6x^2+35x+36[/tex]
Learn more about the area model here;
https://brainly.com/question/19158764
