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Prove. (a-b)^(2)=a^(2)-2*a*b+b^(2)

Prove. (ab)2=a22ab+b2 (a-b)^{2}=a^{2}-2 \cdot a \cdot b+b^{2}

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Q. Prove. (ab)2=a22ab+b2 (a-b)^{2}=a^{2}-2 \cdot a \cdot b+b^{2}
  1. Apply Binomial Square Formula: To expand the expression (ab)2(a-b)^2, we will apply the formula for the square of a binomial, which is (xy)2=x22xy+y2(x-y)^2 = x^2 - 2xy + y^2, where xx and yy are any two terms.
  2. Substitute a and b: Let's substitute aa for xx and bb for yy in the binomial square formula: (ab)2=a22ab+b2(a-b)^{2} = a^{2} - 2ab + b^{2}.
  3. Expand Terms: Now we will expand the terms according to the formula: (ab)2=a22ab+b2(a-b)^2 = a^2 - 2\cdot a\cdot b + b^2.
  4. Final Result: We have successfully expanded the binomial without making any mathematical errors. The expanded form of (ab)2(a-b)^2 is a22ab+b2a^2 - 2ab + b^2.

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