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Add: 2a^2b+5b^2a+7, 3a^2b-2b^2a+6, 8a^2b...

Add: `2a^2b+5b^2a+7`, `3a^2b-2b^2a+6`, `8a^2b-b^2a+9`,

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Add: 3a+b, 2a+4b, 5a-b

If D is the mid-point of the side B C of triangle A B C and A D is perpendicular to A C , then 3b^2=a^2-c ^2 (b) 3a^2=b^2 3c^2 b^2=a^2-c^2 (d) a^2+b^2=5c^2

Calculate: 5a^2b-2a^2b-3a^2b+8a^2b

Let's find the product by successive multiplication____ (2a^3 - 3b^3), (2a^3 + 3b^5) (2a^4 - 3a^2b^2 + b^4)

|{:(" "1+a^2-b^2," "2ab," "-2b),(" "2ab,1-a^2+b^2," "2a),(" "2b," "-2a,1-a^2-b^2):}|=(1+a^2+b^2)^3

Prove that |[2ab,a^2,b^2],[a^2,b^2,2ab],[b^2,2ab,a^2]|=-(a^3+b^3)^2 .

|{:(-a(b^2+c^2-a^2)," "2b^3," "2c^3),(" "2a^3,-b(c^2+a^2-b^2)," "2c^3),(" "2a^3," "2b^3,-c(a^2+b^2-c^2)):}|=abc(a^2+b^2+c^2)^3

Multiply: (a^2-b^2) (2b-6a)

, (a+b)^2 + (a-b)^2 = 2(a^2 + b^2) or (a+b)^2 - (a -b)^2= 4ab or ab = (frac(a+b)(2))^2 -(frac(a-b)(2))^2 to find the following. Let's find 8xy( x^2 + y^2 ) when (x+y) = 5 and (x-y) = 1

prove that , |{:(2ab,a^2,b^2),(a^2,b^2,2ab),(b^2,2ab,a^2):}|=-(a^3+b^3)^2