What do they multiply to?

Algebra Level 2

If ( a − b ) 2 = ( a + b ) 2 (a-b)^2=(a+b)^2 , then what is the value of a b ab ?

undefined 3 0 More than 4 Less than 0 4 1 2

Austin Li by Austin Li , 38, USA

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3 solutions

Austin Li
Jun 16, 2020

(a-b)²=(a+b)²

a²-2ab+b²=a²+2ab+b²

-2ab=2ab

4ab=0

ab=0

either a is 0 or b is 0

Thus, ab=0.

0 Helpful 0 Interesting 1 Brilliant 0 Confused
Mahdi Raza
Jun 16, 2020

\[\begin{align} (a-b)^2 &= (a+b)^2 \\ \cancel{a^2 + b^2} - 2ab &= \cancel{a^2 + b^2} + 2ab \\ -2ab &= 2ab \\ 4ab &= 0 &\blue{\text{Since } 4 \ne 0 \text{ divide the equation by } 4} \\ ab &= \boxed{0}

\end{align}\]

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Zakir Husain
Jun 16, 2020

Starting from the identity: ( a + b ) 2 − ( a − b ) 2 = 4 a b (a+b)^2-(a-b)^2=4ab As ( a + b ) 2 = ( a − b ) 2 ⇒ ( a + b ) 2 − ( a − b ) 2 = 0 (a+b)^2=(a-b)^2 \Rightarrow (a+b)^2-(a-b)^2=0 ⇒ 4 a b = 0 ⇒ a b = 0 \Rightarrow 4ab=0\Rightarrow ab=0

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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