To factor this perfect square, does anyone know how any factors of 49 can possibly equal the sum of 42? I know the answer is (3x+7)^2. Why does it seems like the 42x was disregarded. Can you solve?
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This is a perfect square. A trinomial with two terms with perfect square root. Their product times 2, must make the third term.
Square root of 9x^2 = 3x
Square root of 49 = 7
3x * 7 times 2 = 42x
Then,
(3x + 7)^2 = 9x^2 + 42x + 49
Square root of 9x^2 = 3x
Square root of 49 = 7
3x * 7 times 2 = 42x
Then,
(3x + 7)^2 = 9x^2 + 42x + 49
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9x^2 + 42x + 49
(3x + 7)(3x + 7)
9x^2 + 21x + 21x + 49
(3x + 7)(3x + 7)
9x^2 + 21x + 21x + 49