When given a factored form, we can “undo” the factoring by expanding the two binomials through the FOIL method.
The FOIL method is an acronym for First Outer, Inner Last. This acronym means that we must distribute the first outer term in the first binomial to the terms in the second binomial, and then multiply the second term in the first binomial by the terms in the second binomial. This process is derived from the distributive property.
(2x+3)(3x+5)
The first term in the first binomial is 2x, so 2x must multiply into the terms in the second binomial.
2x•3x+5•2x
6x^2+10x
Then, we must multiply the second term in the first binomial, 3, by the terms in the second binomial.
3•3x+5•3
9x+15
Combine both expansions:
6x^2+10x+9x+15
Combine like terms:
Answer: 6x^2+19x+15