Factorize: `a x+b x+a y+b y` `a x^2+b y^2+b x^2+a y^2` `a^2+b c+a b+a c` `a x-a y+b x-b y`

x+y=a+b , a x-b y=a^2-b^2

x/a-y/b=0 , a x+b y=a^2+b^2

Solve: x+y=a+b ; a x-b y=a^2-b^2

Factorize: 1) x^3-2x^2y+3x y^2-6y^3 2) 6a b-b^2+12 a c-2b c

Factorize: 4x^2+12 x y+9y^2 (ii) x^4-10 x^2y^2+25 y^4 a^4-2a^2b^2+b^4

Prove that |a x-b y-c z a y+b x c x+a z a y+b x b y-c z-a x b z+c y c x+a z b z+c y c z-a x-b y|=(x^2+y^2+z^2)(a^2+b^2+c^2)(a x+b y+c z)dot

Prove that: |a b a x+b y b c b x+c y a x+b y b x+c y0|=(b^2-a c)(a x^2+2b x y+c y^2) .

Divide: x^2-5x+6b y\ x-3 (ii) a x^2-a y^2b y\ a x+a y

The determinant |y^2-x y x^2a b c a ' b ' c '| is equal to a. |b x+a y c x+b y b^(prime)x+a ' y c^(prime)x+b ' y| b. |a x+b y b x+c y a^(prime)x+b ' y b ' x+c ' y| c. |b x+c y a x+b y b^(prime)x+c ' y a^(prime)x+b ' y| d. |a x+b y b x+c y a^(prime)x+b ' y b^(prime)x+c ' y|

Prove that |[a x-b y-c z, a y+b x, c x+a z], [a y+b x, b y-c z-a x, b z+c y],[c x+a z, b z+c y, c z-a x-b y]|=(x^2+y^2+z^2)(a^2+b^2+c^2)(a x+b y+c z)dot