How to Factor Out a Binomial From a Perfect Square Trinomial

Question

I understand how to factor a perfect square trinomial, but I am unable to see the steps taken to go from $$2x(2x + 1) + (2x +1)$$ to $$(2x +1)(2x +1)\text.$$

If you were asked to factor out $2x+1$ from the above expression, what steps would you take to transform it to $$(2x +1)(2x +1)\text?$$

Also, what steps would I need to take to reverse the process? As in to go from $$(2x +1)(2x+1)$$ back to $$2x(2x + 1) + (2x +1)\text.$$

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Answer 1

How to factor out 2x + 1 from the expression

1. divide 2x + 1 from 2x(2x + 1) + 1(2x +1) = 2x + 1
2. Mulitply the divisor by the quotient = (2x +1)(2x + 1)

How to revert the expression back to 2x(2x + 1) + (2x +1)

1. use FOIL or the distributive property to multiply (2x + 1)(2x + 1)

(2x)^2 + 2x + 2x + 1 = 2x(2x + 1) + (2x +1)