Factoring Expressions

Class: Grade 10 FMP Unit 3 Skill

Solutions: 10 FMP Unit 3 Factor Solutions

Review

Skill 3a. Factoring with exponents

Skill 3b: Simplifying algebraic expressions

Use this applet to get the hang of it.

  • Distribute the exponent out of the brackets over the product or division – but not over an addition/subtraction
  • Put any factors with a negative exponent on the bottom if on the top, on the top if on the bottom
  • Simplify factors that have the same base
  • Evaluate any numerical terms

Example:

\big(3x^{-2}y^4\big)^{-4}=3^{-4}x^{8}y^{-16}=\frac{x^8}{81y^{16}}

a little more involved (Example below):

Example:

    \begin{align*} &\Big( \frac{6 \, x^{-2} \, y^5}{4 \, x^5 \, y^{-3}} \Big)^2\\[15pt] =&\frac{6^2}{4^2} \cdot \frac{x^{-4}}{x^{10}} \cdot \frac{y^{10}}{y^{-6}} \\[15pt] =&\frac{36}{16}\cdot x^{-14}\cdot y^{16}\\[15pt] =&\frac{9}{4} \cdot  \frac{1}{x^{14}}\cdot y^{16}\\[15pt] =&\frac{9 \, y^{16}}{4 \, x^{14}}\end{align*}


3. Factors and Products Menu

Next: Area Problems