Advanced Math: Equivalent expressions — Quiz 3

Questions in this quiz (10)

1. Which expression is equivalent to $$(x-7)(3x-2y)-6y(-3x+2y)$$?

   • $$3x^2-2xy-21x+14y+18xy-12y^2$$
   • $$3x^2+16xy-12y^2-21x+14y$$
   • $$3x^2-4xy-12y^2$$
   • $$3x^2+12xy+12y^2$$

2. In the expression $$4(2x^2+px+5)-8x(p+2)$$, $$p$$ is a constant. This expression is equivalent to $$8x^2-12x+20$$. What is the value of $$p$$?

   • $$-2$$
   • $$-1$$
   • $$2$$
   • $$3$$

3. $$(ax+2)(4x^2-bx+3)=8x^3+4x^2+2x+6$$ The equation above is true for all $$x$$. What is the value of $$ab$$?

   • $$2$$
   • $$3$$
   • $$4$$
   • $$8$$

4. The expression $$72y^5-24y^4$$ is equivalent to $$ry^4(3y-1)$$, where $$r$$ is a constant. What is the value of $$r$$?

   • $$12$$
   • $$24$$
   • $$48$$
   • $$72$$

5. Which of the following expressions is equivalent to $$x^2-16$$?

   • $$(x+4)^2$$
   • $$(x-4)^2$$
   • $$(x+4)(x-4)$$
   • $$(x+8)(x-2)$$

6. $$(4200+50y^2)+5(10y^2-40)$$ The expression above can be written in the form $$ay^2+b$$, where $$a$$ and $$b$$ are constants. What is the value of $$a+b$$?

   • $$100$$
   • $$4000$$
   • $$4100$$
   • $$4200$$

7. Which of the following expressions has a factor of $$x+3$$?

   • $$2x^2+9x+18$$
   • $$2x^2+12x+18$$
   • $$2x^2+15x+20$$
   • $$2x^2+18x+18$$

8. Which of the following is equivalent to $$(1-t)(1+t+t^2+t^3+t^4)$$?

   • $$1-t^4$$
   • $$1-t^5$$
   • $$1-t^6$$
   • $$1-t^3$$

9. The expression $$\frac{1}{2}x^2-8$$ can be rewritten as $$\frac{1}{2}(x-k)(x+k)$$, where $$k$$ is a positive constant. What is the value of $$k$$?

   • $$2$$
   • $$4$$
   • $$\sqrt{8}$$
   • $$8$$

10. Which expression is equivalent to $$\frac{30a}{k}+30ak$$, where $$k$$>$$0$$?

    • $$\frac{30a(1+k^2)}{k}$$
    • $$\frac{30ak^2}{k}$$
    • $$\frac{30a(k+1)}{k}$$
    • $$\frac{60a}{k}$$