$$\left(x+y\right)^3=x^3+3x^2y+3xy^2+y^3$$  

$$\left(x+y\right)^3=x^3+x^2y+xy^2+y^3$$  

$$\left(x+y\right)^3=3x^3+x^2y+xy^2+3y^3$$  

$$\left(x+y\right)^3=x^3+3xy+3xy+y^3$$  

$$\left(a+2b\right)^3=a^3+6a^2b+12ab^2+8b^3$$  

$$\left(a+2b\right)^3=a^3+3a^2b+3ab^2+8b^3$$  

$$\left(a+2b\right)^3=a^3+6a^2b+12ab^2+2b^3$$  

$$\left(a+2b\right)^3=3a^3+6a^2b+12ab^2+3b^3$$  

$$\left(a-b\right)^3=a^3-3a^2b+3ab^2-b^3$$  

$$\left(a-b\right)^3=-a^3+3a^2b-3ab^2+b^3$$  

$$\left(a-b\right)^3=a^3-3a^2b-3ab^2+b^3$$  

$$\left(a-b\right)^3=-a^3+3a^2b+3ab^2-b^3$$  

$$\left(3a+5b\right)^3=27a^3+135a^2b+225ab^2+125b^3$$  

$$\left(3a+5b\right)^3=27a^3-135a^2b+225ab^2-125b^3$$  

$$\left(3a+5b\right)^3=-27a^3+135a^2b+225ab^2-125b^3$$  

$$\left(3a+5b\right)^3=3a^3+9a^2b+25ab^2+5b^3$$  

$$\left(a+\frac{1}{2}b\right)^3=a^3+\frac{3}{2}a^2b+\frac{3}{4}ab^2+\frac{1}{8}b^3$$  

$$\left(a+\frac{1}{2}b\right)^3=a^3+3a^2b+3ab^2+\frac{1}{8}b^3$$  

$$\left(a+\frac{1}{2}b\right)^3=a^3+\frac{3}{2}a^2b+\frac{3}{2}ab^2+\frac{1}{4}b^3$$  

$$\left(a+\frac{1}{2}b\right)^3=a^3+\frac{3}{4}a^2b+\frac{3}{8}ab^2+\frac{1}{8}b^3$$  

$$\left(a+b+c\right)^2=a^2+b^2+c^2+2ab+2ac+2bc$$  

$$\left(a+b+c\right)^2=a^2+b^2+c^2+ab+ac+bc$$  

$$\left(a+b+c\right)^2=a^2+b^2+c^2+3ab+3ac+3bc$$  

$$\left(a+b+c\right)^2=a^2+b^2+c^2+3abc$$  

$$\left(a-b+c\right)^2=a^2+b^2+c^2-2ab+2ac-2bc$$  

$$\left(a-b+c\right)^2=a^2-b^2+c^2-2ab+2ac-2bc$$  

$$\left(a-b+c\right)^2=a^2-b^2+c^2+2ab+2ac+2bc$$  

$$\left(a-b+c\right)^2=a^2-b^2+c^2-2ab-2ac-2bc$$  

$$\left(a+2b+3c\right)^2=a^2+4b^2+9c^2+4ab+6ac+12bc$$  

$$\left(a+2b+3c\right)^2=a^2+2b^2+3c^2+2ab+2ac+2bc$$  

$$\left(a+2b+3c\right)^2=a^2+4b^2+9c^2+12ab+24ac+36bc$$  

$$a^3-b^3=\left(a-b\right)\left(a^2+ab+b^2\right)$$  

$$a^3-b^3=\left(a-b\right)\left(a^2-ab+b^2\right)$$  

$$a^3-b^3=\left(a-b\right)\left(-a^2-ab-b^2\right)$$  

$$a^3-b^3=\left(a+b\right)\left(a^2-ab+b^2\right)$$  

$$a^3+b^3=\left(a+b\right)\left(a^2-ab+b^2\right)$$  

$$a^3+b^3=\left(a+b\right)\left(a^2+ab+b^2\right)$$  

$$a^3+b^3=\left(a+b\right)\left(-a^2-ab-b^2\right)$$  

$$a^3+b^3=\left(a-b\right)\left(a^2+ab+b^2\right)$$  

$$\left(\frac{1}{2}xy-3x^2\right)^2=\frac{1}{4}x^2y^2-3x^3y+9x^4$$  

$$\left(\frac{1}{2}xy-3x^2\right)^2=\frac{1}{2}x^2y^2-\frac{3}{2}3x^3y+3x^4$$  

$$\left(\frac{1}{2}xy-3x^2\right)^2=\frac{1}{2}x^2y^2-3x^3y+3x^4$$  

$$\left(\frac{1}{2}xy-3x^2\right)^2=\frac{1}{4}x^2y^2-6x^2y+9x^4$$  

$$\left(\frac{1}{4}a^3+5b^2\right)^2=\frac{1}{16}a^6+\frac{10}{4}a^3b^2+25b^4$$  

$$\left(\frac{1}{4}a^3+5b^2\right)^2=\frac{1}{16}a^9+5a^3b^2+25b^4$$  

$$\left(\frac{1}{4}a^3+5b^2\right)^2=\frac{1}{4}a^9+\frac{10}{4}a^3b^2+5b^4$$  

$$\left(\frac{1}{4}a^3+5b^2\right)^2=\frac{1}{16}a^6+\frac{5}{4}a^3b^2+25b^4$$