<p>Factor.</p><p><code class='latex inline'>\displaystyle x^3 -1 </code></p>

<p>Factor each of the following expressions.</p><p><code class='latex inline'>64x^3 - 125 </code></p>

<p>Factor <code class='latex inline'>\displaystyle x^3 -125 </code></p>

<p>Factor <code class='latex inline'>27y^3-125z^6</code></p>

<p>Factor <code class='latex inline'>x^3 + b^3</code>.</p>

<p>Factor the difference of cubes.</p><p><code class='latex inline'>\displaystyle 64x^3 -27 </code></p>

<p>Factor</p> <ul> <li>i) <code class='latex inline'>\displaystyle 8x^3 +1 </code></li> <li>ii) <code class='latex inline'>125x^6 + 8</code></li> <li>iii) <code class='latex inline'>64x^{12} +27</code></li> <li>iv) <code class='latex inline'>\frac{8}{125}x^{3} +64y^6</code></li> </ul>

<p><strong>(a)</strong> Factor each sum of cubes.</p><p><code class='latex inline'> \displaystyle \begin{array}{cccc} &(i) &x^3 + 1 &(ii) & x^3 + 8\\ &(iii) &x^3 + 27 & (ii) & x^3 + 64 \\ \end{array} </code></p><p><strong>(b)</strong> Use the results of a part (a) to predict a pattern for factoring <code class='latex inline'>x^3 + a^3.</code></p>

<p>Factor each of the following expressions.</p><p><code class='latex inline'>1000x^3 + 729</code></p>

<p> If <code class='latex inline'>\displaystyle \frac{1}{a + c} = \frac{1}{a} + \frac{1}{c}</code>, find <code class='latex inline'>(a/c)^3</code>.</p><p><a href="https://www.youtube.com/watch?v=1g9XZknJJs8">Futher Hint</a></p>

<p>Factor <code class='latex inline'>x^3 - 125 </code>. Verify your answer by expanding.</p>

<p>Factor <code class='latex inline'>x^3 - a^3</code>.</p>

<p>Factor <code class='latex inline'>\displaystyle x^3 +125 </code></p>

<p>Show that </p><p><code class='latex inline'>x^3-1=(x-1)(x^2+x+1)</code>.</p>

<p>Factor each of the following expressions.</p><p><code class='latex inline'>8x^3 - 27 </code></p>

<p>What are the factors of <code class='latex inline'>\displaystyle (x+3)^{3}+8 </code> ?</p><p>a) <code class='latex inline'>\displaystyle \left(x^{3}+27\right)(8) </code></p><p>b) <code class='latex inline'>\displaystyle (x+3)\left(x^{2}-3 x+17\right) </code></p><p>c) <code class='latex inline'>\displaystyle (x+5)\left(x^{2}+4 x+7\right) </code></p><p>d) <code class='latex inline'>\displaystyle (x+1)\left(x^{2}-4 x+7\right) </code></p>

<p>Factor the difference of cubes.</p><p><code class='latex inline'>\displaystyle 512x^3 - 125 </code></p>

<p>Factor each of the following expressions.</p><p><code class='latex inline'>x^3 - 125</code></p>

<p>Factor <code class='latex inline'>y^3-27</code>.</p>

<p>Factor <code class='latex inline'>m^3-64</code></p>

<p>Factor each of the following expressions.</p><p><code class='latex inline'>216x^3 -1</code></p>

<p>Factor the difference of cubes.</p><p><code class='latex inline'>\displaystyle 343x^3 -1728 </code></p>

<p>Show that <code class='latex inline'>a^3+1000=(a+10)(a^2-10a+100)</code>.</p>

<p>Factor <code class='latex inline'>k^6+216e^3</code></p>

<p>Factor each of the following expressions.</p><p><code class='latex inline'>(x + 5)^3-(2x + 1)^3</code></p>

<p>Factor each of the following expressions.</p><p><code class='latex inline'>125x^3 - 512</code></p>

<p>Factor.</p><p><code class='latex inline'>\displaystyle x^3 + 64 </code></p>

<p>Factor the difference of cubes.</p><p><code class='latex inline'>\displaystyle 1331x^3 -1 </code></p>

<p>Factor each of the following expressions.</p><p><code class='latex inline'>64x^3 - 1331</code></p>

<p>Factor <code class='latex inline'>x^3 + 125</code>. Verify your answer by expanding.</p>

<p>Factor each differences of cubes.</p> <ul> <li><strong>i.</strong> <code class='latex inline'>x^3 -1</code></li> <li><strong>ii.</strong> <code class='latex inline'>x^3 -8</code></li> <li><strong>iii.</strong> <code class='latex inline'>x^3 -27</code></li> <li><strong>iv.</strong> <code class='latex inline'>x^3 -64</code></li> </ul>

<p>Factor each of the following expressions.</p><p><code class='latex inline'>27x^3 + 8 </code></p>

<p>Factor <code class='latex inline'>y^3+27</code></p>

<p>Factor each of the following expressions.</p><p><code class='latex inline'>x^3 + 8</code></p>

<p>Factor each of the following expressions.</p><p><code class='latex inline'>\displaystyle -432x^5 - 128x^2 </code></p>

<p>Solve by factoring.</p><p><code class='latex inline'>8x^4 - 64x= 0</code></p>

<p>Factor the sum of cubes.</p><p><code class='latex inline'>\displaystyle 1728x^3 + 125 </code></p>

<p>Dan claims that the equation below is true.</p><p><code class='latex inline'>\displaystyle \frac{(a + b)(a^2 -ab + b^2) + (a -b)(a^2 + ab + b^2)}{2a^3} = 1 </code></p><p>Do you agree or disagree with Dan? Justify your decision.</p>

<p>Factor each of the following expressions.</p><p><code class='latex inline'>64x^3 + 27y^3</code></p>

<p>Factor each difference of cubes.</p><p>i) <code class='latex inline'>\displaystyle x^3 -1 </code></p><p>ii) <code class='latex inline'>\displaystyle x^3 -8 </code></p><p>iii) <code class='latex inline'>\displaystyle x^3 -27 </code></p><p>iv) <code class='latex inline'>\displaystyle x^3 -64 </code></p>

<p>Factor each of the following expressions.</p><p><code class='latex inline'>x^3 -343</code></p>

<p>Factor <code class='latex inline'>343q^{12}+729r^{24}</code></p>

<p>Factor <code class='latex inline'>\displaystyle x^3 -a^3 </code></p>

<p>Factor each of the following expressions.</p><p><code class='latex inline'>x^3 - 64</code></p>

<p>Factor each of the following expressions.</p><p><code class='latex inline'>\displaystyle \frac{1}{27}x^3 - \frac{8}{125} </code></p>

<p>Andrew claims that the following statement is true: <code class='latex inline'>x^3 - y^3 = (x - y)(x^2 + y^2)</code></p><p>Is Andrew correct? Justify your decision. </p>

<p>Factor the sum of cubes.</p><p><code class='latex inline'>\displaystyle 1000x^3 + 343 </code></p>

<p>1729 is a very interesting number. It is the smallest whole number that can be expressed as a sum of two cubes in two ways: <code class='latex inline'>1^3 + 12^3</code> and <code class='latex inline'>9^3 + 10^3</code>. </p><p>Show that they are equal by factoring.</p>

<p>a) Factor each sum of cubes.</p> <ul> <li>i) <code class='latex inline'>\displaystyle x^3 +1 </code></li> <li>ii) <code class='latex inline'>x^3 + 8</code></li> <li>iii) <code class='latex inline'>64x^{12}-27</code></li> <li>iv) <code class='latex inline'>\frac{8}{125}x^{3}-64y^6</code></li> </ul> <p>b) Factor <code class='latex inline'>\displaystyle x^3 + a^3 </code></p>

<p>Factor the sum of cubes.</p><p><code class='latex inline'>\displaystyle 216x^3 + 2197 </code></p>

<p>Factor.</p><p><code class='latex inline'>\dfrac{x^6}{16}-\dfrac{y^6}{25}</code></p>

<p>Factor full.</p><p><code class='latex inline'>216x^3 -8</code></p>

<p>Factor each of the following expressions.</p><p><code class='latex inline'>512 - 1331x^3</code></p>

<p>Factor each of the following expressions.</p><p><code class='latex inline'>1331x^3 + 1728</code></p>

<p>Factor each of the following expressions.</p><p><code class='latex inline'>x^3 + 1 </code></p>

<p>Factor each of the following expressions.</p><p><code class='latex inline'>512x^3 + 1</code></p>

<p>Factor each of the following expressions.</p><p><code class='latex inline'>343x^3 + 27</code></p>

<p>Factor each of the following expressions.</p><p><code class='latex inline'>x^3 +1000</code></p>

<p>Determine if <code class='latex inline'>x + 3</code> is a factor of <code class='latex inline'>\displaystyle x^3 +27 </code></p>

<p>What is <code class='latex inline'>\displaystyle 27 x^{3}-216 </code> in factored form?</p><p>a) <code class='latex inline'>\displaystyle 3(x-2)\left(x^{2}+2 x+4\right) </code></p><p>b) <code class='latex inline'>\displaystyle 27(x+2)\left(x^{2}-2 x+4\right) </code></p><p>c) <code class='latex inline'>\displaystyle 27(x-2)\left(x^{2}+2 x+4\right) </code></p><p>d) <code class='latex inline'>\displaystyle (3 x+6)\left(9 x^{2}-18 x+36\right) </code></p>

<p>Factor the sum of cubes.</p><p><code class='latex inline'>\displaystyle 27x^3 + 1331 </code></p>

<p> Show that <code class='latex inline'>x^3-8=(x-2)(x^2+2x+4).</code></p>