A:B=2:3

Fill in the blanks : If A:B = 3:2, B:C = 3:5 then A:B:C =_______

If a:b=2:5 then (3a+4b):(4a+5b)=

Incorrect: (2a+3b)(a-b)=2a^2+ab-3b^2 Correct: (2a+3b)(a-b)=2a^2+3ab-2ab-3b^2=2a^2+ab-3b^2 .

If A and B be square matrices of the same order such that BA=AB, prove that : (A+B)^3 = A^3 + 3A^2B + 3AB^2 +B^3

If a:b = 3 : 2 and b : c = 2 : 5, find a : c.

If A and B are square matrices of the same order such that AB=BA, then (A) (A-B)(A+B)=A^2-B^2 (B) (A+B)^2=A^2+2AB+B^2 (C) (A+B)^3=A^3A^2B+3AB^2+B^3 (D) (AB)^2=A^2B^2

If A and B are square matrices of the same order such that AB=BA, then (A) (A-B)(A+B)=A^2-B^2 (B) (A+B)^2=A^2+2AB+B^2 (C) (A+B)^3=A^3A^2B+3AB^2+B^3 (D) (AB)^2=A^2B^2

Find the value of the following expressions at a=1 b = -2 : (i) a^2+b^2+3ab (ii) a^3+a^2b+ab^2+b^3