Question

Explain factorization of a algebraic expressions ?

Answer 1

Factorization in algebraic expressions is all about the reverse process of multiplication.
Algebraic Identities
If an equality holds true for all values of the variable, then it is called an Identity.
Identity 1: $(x+y{)}^2=x^2+2xy+y^2$
Identity 2: $(x-y{)}^2=x^2-2xy+y^2$
Identity 3: $x+y\left)\right(x-y)=x^2-y^2$
Identity 4: $(x+y+z{)}^2=x^2+y^2+z^2+2xy+2yz+2zx$
Identity 5: $(x+y{)}^3=x^3+y^3+3xy(x+y)$
Identity 6: $(x-y{)}^3=x^3-y^3-3xy(x-y)$
Identity 7: $x^3+y^3=(x+y)(x^2-xy+y^2)$
Identity 8: $x^3-y^3=(x-y)(x^2+xy+y^2)$
Identity 9: $=x^3+y^3+z^2-3xyz=(x+y+z)(x^2+y^2+z^2-xy-yz-zx)$
$=\frac{1}{2}(x+y+z)\left\{\right(x-y{)}^2+(y-z{)}^2+(z-x{)}^2\}$