Question

Given the following perfect square trinomial, fill in the missing term. (Do not type the variable in the blank.)

4x2 + ___x + 49

help I will award medals

Answer 1

If it's a perfect square, the leading term must be the square of the leading term of the product binomial. So \(4x^2 = a^2, a =\)

Answer 2

Similarly, the constant term must be the square of the constant term of the product binomial, so \(49 = b^2, b =\)

Answer 3

And \[(a+b)^2 = (a+b)(a+b) = a(a+b) + b(a+b) = a^2+ab + ab + b^2 \]\[= a^2+2ab + b^2\]So the middle term (aka the missing term) = \(2 a b\) where \(a,b\) are the values you found earlier...

Answer 4

(don't forget to remove the \(x\) when typing in the answer!\)

Answer 5

4x^2+2x+49?

Answer 6

If \[a^2 = 4x^2\]take square root of both sides\[\sqrt{a^2}=\sqrt{4x^2}\]\[a = \sqrt{4}*\sqrt{x^2} = 2x\]right?

Answer 7

if \[b^2=49\]take square root of both sides\[\sqrt{b^2} = \sqrt{49}\]\[b = \sqrt{49}\]\[b=7\]right?

Answer 8

missing term is then\[2ab = 2(2x)(7) =\]

Answer 9

So the answer should be 4x^2+2x+49

Answer 10

No! what is \(2(2x)(7)\)

Answer 11

What?

Answer 12

what is \(2*2x*7\)

Answer 13

28x

Answer 14

Right! so the missing term is \(28x\). Here, let me show you. We have a perfect square trinomial, which means we have \((a+b)^2 = 4x^2 + <something> + 49\) and we established that \(a = 2x,~b = 7\)

That gives us
\[(2x+7)(2x+7) = 2x(2x+7)+7(2x+7) = 4x^2 + 14x + 14x + 49 \]\[=4x^2 + 28x + 49\]
Therefore \(28x\) is the missing term, and you enter "28" as your answer (because they don't want you to include the variable, \(x\).

Answer 15

Thanks

Answer 16

when you square a binomial, the middle term is always 2 * first term * second term. We just had to puzzle out what the first and second terms must have been...