Divide: `(a^2+2a b+b^2)-(a^2+2a c+c^2)b y\ 2a+b+c`

Divide : 4a^(2) + 12ab + 9b^(2) - 25c^(2) by 2a + 3b + 5c

Divide: 35 a^2+32 a-99\ b y\ 7a-9 a x^2+(b+a c)x+b c\ b y\ x+c

Prove: |(a^2,b c, a c+c^2),(a^2+a b,b^2,a c ),(a b,b^2+b c,c^2)|=4a^2b^2c^2

If a ,b ,c in R^+ , then the minimum value of a(b^2+c^2)+b(c^2+a^2)+c(a^2+b^2) is equal to (a) a b c (b) 2a b c (c) 3a b c (d) 6a b c

Show that: |(b+c)^2b a c a a b(c+a)^2c b a c b c(a+b)^2|=2a b c(a+b+c)^3

Divide: x^4-y^4b y\ x^2-y^2 (ii) a c x^2+\ (b c+a d)x+b d\ b y\ (a x+b)

Identify the like terms in the following algebraic expressions: (i) a^2+b^2-2a^2+c^2+4a (ii) 3x+4x y-2y z+5/2z y (iii) a b c+a b^2c+2a c b^2+3c^2a b+b^2a c-2a^2b c+3c a b^2

The area of a parallelogram formed by the lines a x+-b y+-c=0 is (a) (c^2)/((a b)) (b) (2c^2)/((a b)) (c) (c^2)/(2a b) (d) none of these

Suppose A, B, C are defined as A=a^2b+a b^2-a^2c-a c^2 , B=b^2c+b c^2-a^2b-a b^2,and C=a^2c +'a c^2-b^2' c-b c^2, w h e r ea > b > c >0 and the equation A x^2+B x+C=0 has equal roots, then a ,b ,c are in AdotPdot b. GdotPdot c. HdotPdot d. AdotGdotPdot

Prove: |((b+c)^2, a^2, b c) ,((c+a)^2, b^2 ,c a),( (a+b)^2, c^2, a b)|=(a-b)(b-c)(c-a)(a+b+c)(a^2+b^2+c^2) .