Answer:
[tex](x-3)(x-9)(x-4)=x^3-16x^2+75x-108[/tex]
Step-by-step explanation:
Given:
The expression to expand is given as:
[tex](x-3)(x-9)(x-4)[/tex]
Let us expand the first two binomials of the given expression using FOIL method.
The FOIL method states that:
[tex](a + b)(c + d) = ac + ad + bc + bd[/tex]
[tex](x-3)(x-9)=(x\times x)+(x\times -9)+(-3\times x)+(-3\times -9)\\\\(x-3)(x-9)=x^2-9x-3x+27=x^2-12x+27[/tex]
Now, let us multiply the result with the remaining binomial. Multiplying each term of the trinomial with each term of the binomial, we get:
[tex](x^2-12x+27)(x-4)\\\\= (x^2\times x)+ (x^2\times -4)+(-12x\times x)+(-12x\times -4)+(27\times x)+(27\times -4)\\\\=x^3-4x^2-12x^2+48x+27x-108\\\\=x^3-16x^2+75x-108...........(\because-12x^2-4x^2=-16x^2,48x+27x=75x)[/tex]
Therefore, the equivalent expression after expanding is given as:
[tex](x-3)(x-9)(x-4)=x^3-16x^2+75x-108[/tex]
