Verify the Identity a^2-b^2=(a+b)(a-b)

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Trigonometry

$a^{2} - b^{2} = (a + b) (a - b)$

Simplify the right side.

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Simplify $(a + b) (a - b)$ .

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Expand $(a + b) (a - b)$ using the FOIL Method.

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Apply the distributive property.

$a^{2} - b^{2} = a (a - b) + b (a - b)$

Apply the distributive property.

$a^{2} - b^{2} = a \cdot a + a (- b) + b (a - b)$

Apply the distributive property.

$a^{2} - b^{2} = a \cdot a + a (- b) + b a + b (- b)$

Simplify terms.

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Combine the opposite terms in $a \cdot a + a (- b) + b a + b (- b)$ .

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Reorder the factors in the terms $a (- b)$ and $b a$ .

$a^{2} - b^{2} = a \cdot a - a b + a b + b (- b)$

Add $- a b$ and $a b$ .

$a^{2} - b^{2} = a \cdot a + 0 + b (- b)$

Add $a \cdot a$ and $0$ .

$a^{2} - b^{2} = a \cdot a + b (- b)$

Simplify each term.

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Multiply $a$ by $a$ .

$a^{2} - b^{2} = a^{2} + b (- b)$

Rewrite using the commutative property of multiplication.

$a^{2} - b^{2} = a^{2} - b \cdot b$

Multiply $b$ by $b$ by adding the exponents.

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Move $b$ .

$a^{2} - b^{2} = a^{2} - (b \cdot b)$

Multiply $b$ by $b$ .

$a^{2} - b^{2} = a^{2} - b^{2}$

Since the two sides have been shown to be equivalent, the equation is an identity.

$a^{2} - b^{2} = (a + b) (a - b)$ is an identity.

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Name

Name	one billion eight hundred ninety-four million nine hundred thirty-eight thousand three hundred thirty-six

Interesting facts

1894938336 has 256 divisors, whose sum is 25581671424
The reverse of 1894938336 is 6338394981
Previous prime number is 3

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 54
Digital Root 9

Name

Name	one billion one hundred thirty-seven million one hundred fifty thousand three hundred forty-nine

Interesting facts

1137150349 has 16 divisors, whose sum is 1266012720
The reverse of 1137150349 is 9430517311
Previous prime number is 61

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 34
Digital Root 7

Name

Name	one billion six hundred six million one hundred fifty-six thousand five hundred fifty-seven

Interesting facts

1606156557 has 4 divisors, whose sum is 2141542080
The reverse of 1606156557 is 7556516061
Previous prime number is 3

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 42
Digital Root 6

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