Algebraic Manipulation: Squares & Corollaries

Proof: (a+b)²​ = (a+b)(a+b) = a(a+b) + b(a+b) = a²​ + ab + ab + b²​ = a2​ + 2ab + b2​ 

Problem 1.1: Find the square of 3a + 5b using formula.

Solution: (3a + 5b)² = (3a)² + 2 $\times$ 3a $\times$ 5b + (5b)² = 9a² + 30ab + 25b² 

Problem 1.2: Find the square of 105 using formula.

Solution: (105)² = (100 + 5)² = 

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Formula #2: (a-b)2 = a2 - 2ab + b2​ 

Problem 2.1: Find the square of 3p-2q using formula.

Solution: 

Problem 2.2: Find the square of -x-y using formula.

Solution:

Problem 2.3: Find the square of 97 using formula.

Solution: (97)² = (100-3)² 

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So far, we learned to use the two most basic formula's of squaring using two term expressions. Now, lets use these formula's to square expressions having three terms.

Problem 3.1: Find the square of a+b+c using formula.

Problem 3.2: Find the square of a-b-c using formula.

Problem 3.3: Find the square of a-b+c using formula.

Problem 3.4: Find the square of a+b-c using formula.