﻿ Writing Expressions in the form A^2
WRITING EXPRESSIONS IN THE FORM $\,A^2\,$
by Dr. Carol JVF Burns (website creator)
Follow along with the highlighted text while you listen!
• PRACTICE (online exercises and printable worksheets)
• Need some simpler practice with perfect squares first?

For this lesson, you'll need these exponent laws:

$(xy)^m = x^m y^m$
$(x^m)^n = x^{mn}$
You'll be using them ‘backwards’that is, from right-to-left.

That is, you'll be starting with an expression of the form $\,x^my^m\,$,
and rewriting it in the form $\,(xy)^m\,$.

Or, you'll be starting with an expression of the form $\,x^{mn}\,$,
and rewriting it in the form $\,(x^m)^n\,$.

Here, you will practice writing expressions in the form $\,A^2\,$.
Only whole number coefficients and exponents are used in this exercise.
(The whole numbers are: $\,0, 1, 2, 3, \ldots\,$)

EXAMPLES:
Question: Write $\,9\,$ in the form $\,A^2\,$.
Answer: $9 = 3^2$
Question: Write $\,9x^2\,$ in the form $\,A^2\,$.
Answer: $9x^2 = 3^2x^2 = (3x)^2$
Question: Write $\,x^6\,$ in the form $\,A^2\,$.
Answer: $x^6 = x^{3\cdot 2} = (x^3)^2$
Question: Write $\,16x^4\,$ in the form $\,A^2\,$.
Answer: $\cssId{s31}{16x^4} \cssId{s32}{= 4^2\cdot x^{2\cdot 2}} \cssId{s33}{= 4^2 (x^2)^2} \cssId{s34}{= (4x^2)^2}$
Question: Write $\,-16\,$ in the form $\,A^2\,$.
Answer: not possible; a negative number can't be a perfect square
Question: Write $\,16x^3\,$ in the form $\,A^2\,$.
Answer: not possible using only whole numbers, since $\,3\,$ isn't a multiple of $\,2\,$
Master the ideas from this section

When you're done practicing, move on to:
Factoring a Difference of Squares

CONCEPT QUESTIONS EXERCISE:
 If possible, write in the form $\,A^2\,$: