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Advanced Math / Equivalent expressions Difficulty: Hard

$open parenthesis, 7,532, plus 100 y squared, close parenthesis, plus, 10 times open parenthesis, 10 y squared minus 110, close parenthesis$

The expression above can be written in the form $a, times y squared, plus b$ , where a and b are constants. What is the value of $a, plus b$ ?

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Explanation

The correct answer is 6632. Applying the distributive property to the expression yields $open parenthesis, 7532 plus 100 y squared, close parenthesis, plus, open parenthesis, 100 y squared, minus 1100, close parenthesis$ . Then adding together $7532 plus 100 y squared$ and $100 y squared, minus 1100$ and collecting like terms results in $200 y squared, plus 6432$ . This is written in the form $a, y squared, plus b$ , where $a, equals 200$ and $b equals 6432$ . Therefore $a, plus b equals, 200 plus 6432, which equals 6632$ .