Property 10
BINOMIAL EXPONSION
Pascal’s Triangle
\(\left(a+b\right)^1=a+b\)
\(\left(a+b\right)^2=a^2+2ab+b^2\)
\(\left(a+b\right)^3=a^3+3a^2b+3ab^2+b^3\)
\(\left(a-b\right)^2=a^2-2ab+b^2\)
\(\left(a-b\right)^3=a^3-3a^2b+3ab^2-b^3\)
\(\left(a-b\right)^4=a^4-4a^3b+6a^2b^2-4ab^3+b^4\)
1.
\(\left(a+b\right)^3=?\)
2.
\(a^3-3a^2b+3ab^2-b^3=8\)
\(\Rightarrow a-b=?\)
3.
\(x^3-6x^2+12x-8=27\)
\(\Rightarrow x=?\)
4.
\(8x^3+12x^2+6x+1=125\)
\(\Rightarrow x=?\)
5.
\(\samefrac{x^3+3x^2+3x+1}{x^2+2x+1}=?\)
6.
\(\samefrac{x^3-9x^2y+27xy^2-27y^3}{\left(x-3y\right)^2}=?\)
7.
\(\samefrac{x^3+9x^2+27x+27}{x^2+6x+9}=?\)
8.
\(x^3-9x^2y+27xy^2-27y^3=8\)
\(\Rightarrow x-3y=?\)
9.
\(8a^3+12a^2b+6ab^2+b^3=64\)
\(b=1\)
\(\Rightarrow a=?\)
10.
\(a^3+3ab^2=8\)
\(b^3+3a^2b=7\)
\(\Rightarrow a-b=?\)
11.
\(a^3+3a^2b=20\)
\(b^3+3ab^2=7\)
\(\Rightarrow a+b=?\)
12.
\(x>y\)
\(x^4-4x^3y+6x^2y^2-4xy^3+y^4=16\)
\(\Rightarrow x-y=?\)
13.
\(x^5-5x^4+10x^3-10x^2+5x-1=32\)
\(\Rightarrow x=?\)
14.
\(x+y=4\)
\(x\cdot y=2\)
\(\Rightarrow x^3+y^3=?\)
15.
\(x-y=3\)
\(x\cdot y=1\)
\(\Rightarrow x^3-y^3=?\)