Question

Can anybody do this sat problem for me? Show your work. (Extra points offered)

Answer 1

Answer:

B) -3

Step-by-step explanation:

$(4x+4)(ax-1)-x^2+4\qquad\text{use FOIL}\ (a+b)(c+d)=ac+ad+bc+bd\\\\=(4x)(ax)+(4x)(-1)+(4)(ax)+(4)(-1)-x^2+4\\\\=4ax^2-4x+4ax-4-x^2+4\qquad\text{combine like terms}\\\\=(4a-1)x^2+(-4+4a)x+(-4+4)\\\\=(4a-1)x^2+(4a-4)x\\\\\text{Given expression is equvalent to}\ bx.$

$(4a-1)x^2+(4a-4)x=bx\\\\(4a-1)x^2+(4a-4)x=0x^2+bx\\\\\text{Therefore}\\\\4a-1=0\ \text{and}\ 4a-4=b\\\\4a-1=0\qquad\text{add 1 to both sides}\\\\4a=1\qquad\text{divide both sides by 4}\\\\a=\dfrac{1}{4}\\\\\text{Substitute to the second equation and solve for}\ b:\\\\4\left(\dfrac{1}{4}\right)-4=b\\\\1-4=b\\\\-3=b\to b=-3$