If a model is made for a square of side \((5a+2)\), what is the total area?

Correct answer: \(25a^2+20a+4\)

Answer: B, \(25a^2+20a+4\). A square’s area is side multiplied by itself, so the required expression is \((5a+2)^2\). Use the identity \((u+v)^2=u^2+2uv+v^2\), with \(u=5a\) and \(v=2\). Then \(u^2=25a^2\), the two mixed rectangles together give \(2uv=2(5a)(2)=20a\), and the small square gives \(v^2=4\). Adding these parts gives \(25a^2+20a+4\). Thus B is correct. A has only \(10a\), as though one mixed rectangle had been counted instead of two. C incorrectly squares \(5a\) as \(5a^2\) instead of \(25a^2\). D uses 2 instead of the constant square \(2^2=4\). Memory cue: the middle term of a binomial square is twice the product of the two parts.