Lesson 1 Equivalent Expressions

3m+13

3m-7

3m+3

11m-40

11m-55

-2+4x

2-6x

8-5x

3-x

9-6x

$$4x^2+5x+6$$  

$$3x^2+9x+6$$  

$$3x^2+9x-6$$  

$$2x^2+9x-6$$  

$$2x^2-5x+6$$  

$$\left(-x\right)^2$$   

$$-x^2$$   

$$-x$$   

$$x^{-2}$$   

x 

$$7a^2+5a$$  

$$a^2+5a+2b$$  

$$-a^2+5a-b^2$$  

$$-a\left(a+5\right)$$  

$$-a\left(a-5\right)$$  

$$\left(xy-16\right)\left(xy+1\right)$$  

$$\left(xy-8\right)^2$$  

$$\left(xy-8\right)\left(xy+8\right)$$  

$$\left(xy-4\right)\left(xy+4\right)$$  

$$\left(xy-4\right)^2$$  

$$2x^2-y^2$$  

$$2x^3-y^2$$  

$$2x^3+xy-y^2$$  

$$2x^3+2xy-x^2y^2$$  

$$2x^3-x^2y+2xy-y^2$$  

$$x^2$$  

$$5x^2-12x-7$$  

$$5x^2+12$$  

$$6x^2-17x+12$$  

$$6x^2+12$$  

$$4\ \frac{2}{3}a$$  

$$7a$$  

$$7\ \frac{1}{3}a$$  

$$7\ \frac{3}{4}a$$  

$$15\ \frac{1}{2}a$$  

$$\frac{8}{4x}$$  

$$\frac{15}{4x}$$  

$$\frac{8}{4+x}$$  

$$\frac{5x+12}{4+x}$$  

$$\frac{3x+20}{4x}$$  

all positive real numbers

all negative real numbers

2 only

1/2 only

-1/2 only

$$x^2-2$$  

$$x^2+2$$  

$$x-\sqrt[]{2}$$  

$$x+\sqrt[]{2}$$  

x-2

$$\frac{19ab}{2ab}$$  

$$\frac{9a+10b}{2ab}$$  

$$\frac{14}{a+2b}$$  

9a-10b

$$\left(x^2+5\right)\left(x^2-3\right)$$  

$$\left(3x^2-15\right)\left(x^2+3\right)$$  

$$3\left(x^4+6x^2-45\right)$$  

$$3\left(x^2-5\right)\left(x^2+3\right)$$  

$$3\left(x^2+5\right)\left(x^2-3\right)$$