Perfect Squares with Coefficients Other than 1

9.4.1 Perfect Squares with Coefficients Other than 1

9.4.1 • Perfect Squares with Coefficients Other than 1

Elena says, " $(x + 3)^{2}$ can be expanded into $x^{2} + 6 x + 9$ . Likewise, $(2 x + 3)^{2}$ can be expanded into $4 x^{2} + 6 x + 9$ ."

Find an error in Elena's statement and correct the error. Show your reasoning.

Compare your answer:

$(2 x + 3)^{2}$ is not equivalent to $4 x^{2} + 6 x + 9$ .

Applying the distributive property to $(2 x + 3) (2 x + 3)$ gives $4 x^{2} + 6 x + 6 x + 9$ , which is $4 x^{2} + 12 x + 9$ .