Question

Use the foil method to find the product:

Answer 1

$\text{FOIL method:}\ (a+b)(c+d)=ac+ad+bc+bd\\\\(q-3)(q-4)=(q)(q)+(q)(-4)+(-3)(q)+(-3)(-4)\\\\=q^2-4q-3q+12=\boxed{q^2-7q+12}\\--------------------------------\\(t+2)(2t+1)=(t)(2t)+(t)(1)+(2)(2t)+(2)(1)\\\\=2t^2+t+4t+2=\boxed{2t^2+5t+2}\\--------------------------------\\(3+i)(i^2+8i-2)=(3)(i^2)+(3)(8i)+(3)(-2)+(i)(i^2)+(i)(8i)+(i)(-2)\\\\=3i^2+24i-6+i^3+8i^2-2i=\boxed{i^3+11i^2+22i-6}\\--------------------------------$

$(b-4)(5b^2-5b+4)\\\\=(b)(5b^2)+(b)(-5b)+(b)(4)+(-4)(5b^2)+(-4)(-5b)+(-4)(4)\\\\=5b^3-5b^2+4b-20b^2+20b-16=\boxed{5b^3-25b^2+24b-16}$