A student claims that $(x+4)^2=x^2+16$. Expand $(x+4)^2$ correctly and identify the missing

Question

A student claims that $(x+4)^2=x^2+16$. Expand $(x+4)^2$ correctly and identify the missing term. Find every value of $x$ for which the student’s incorrect formula happens to give the correct result. For real numbers $a$ and $b$, explain exactly when $ (a+b)^2=a^2+b^2 $ is true.

Accepted Answer

(a) $x^2+8x+16$; Missing $8x$. (b) $x=0$. (c) Exactly when $a=0$ or $b=0$, including both zero.

Quadratic Functions, Equations and Inequalities

Quadratic Functions, Equations and Inequalities