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Algebra
Pregunta

3. When working with quadratics, we often use the ...

3. When working with quadratics, we often use the identity \( a ^ { 2 } - b ^ { 2 } = ( a + b ) ( a - b ) \) to factor quadratic expressions of such \( _ { a } \) form. Using what you've learned about rationalizing denominators and complex conjugates, find and prove identities to easily factor expressions of these forms: 

a. \( a ^ { 2 } + b ^ { 2 } \) 

b. \( a ^ { 2 } - b \) 

Hint: your factored forms may look very similar to the factored form of \( a ^ { 2 } - b ^ { 2 }\) 

Answer

(a) \(a^2+ b^2 = (a + b + \sqrt{2ab} )(a + b - \sqrt{2ab})\) or \(a^2 - b^2 = (a+ ib)(a- ib)\)

 

(b) \(a^2 - b^2 = (a+ b)(a- b)\)

Solución
View full explanation on CameraMath App.