Polynomial Arithmetic: Applying the Perfect Square Identity

Algebra Level 1

What is the coefficient of $x$ in the expansion of $(x+3 ) ^ 2$ ?

3 solutions

Brilliant Mathematics Staff
Aug 1, 2020

$(x+3)^2 = x \times x + 2 \times 3 \times x + 3 \times 3 = x^2 + 6 x + 9.$

Hence, the coefficient of $x$ is 6.

Mahdi Raza
Aug 20, 2020

$(x+3)^2 = x^2 + {\red{6}}x + 9 \quad \implies \boxed{{\red{6}}}$

Yajat Shamji
Aug 2, 2020

$(x + 3)^2 = 2(3x) = \fbox 6$

In general:

$(x + a)^2 = x^2 + 2(ax) + a^2$

Yajat Shamji - 10 months, 2 weeks ago

Hi Yajat. $(x+3)^2 = 2(3x)$ is not an algebraic identity. Consider $x = 0$ . The left-hand-side is equal to 9, but the right-hand-side is equal to 0.

Brilliant Mathematics Staff - 10 months, 2 weeks ago

No. Just using algebra, is this true?

Yajat Shamji - 10 months, 2 weeks ago

@Yajat Shamji – Hi Yajat, $(x+3)^2$ is equal to $x^2 + 6x + 9$ , but it does not equal to $2(3x)$ .

Brilliant Mathematics Staff - 10 months, 2 weeks ago

No assigning values.

Yajat Shamji - 10 months, 2 weeks ago