Question

Find the missing number that makes the expression a perfect square.

B. 9x² +42x+____

Answer 1

• The missing number is 49

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Use the square of the sum identity:

• (a + b)² = a² + 2ab + b²

Comparing the given incomplete expression with the identity we can see:

• a² = 9x² ⇒ a = 3x

and

• 2ab = 42x,

Substitute the value of a into the last equation to find the value of b:

• 2*3x*b = 42x
• 6x*b = 42x
• b = 7

So the missing part of the perfect square expression is:

• b² = 7² = 49

The full expression is now:

• 9x² + 42x + 49 = (3x + 7)²