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      <text>1.3.1.a</text>
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      <text><![CDATA[<h3>1. Addition and subtraction of like terms</h3>
<p><strong>Like terms</strong> are multiples of the same quantity. For example \(5y\), \(17y\) and \({1\over 2} y\) are all multiples of \(y\) and so are like terms. Similarly, \(3x^2\), \(-5x^2\) and \({1\over 4}x^2\) are all multiples of \(x^2\) and so are like terms.<br><br>Further examples of like terms are:<br><br>\(kx\) and \(\ell x\) which are both multiples of \(x\),<br><br>\(x^2y\), \(6x^2y\), \(-13x^2y\), \(-2yx^2\), which are all multiples of \(x^2y,\)<br><br>\(abc^2\), \(-7abc^2\), \(kabc^2\), are all multiples of \(abc^2\)<br><br>Like terms can be added or subtracted in order to simplify expressions.</p>

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<h4 class="HELM_example">Example</h4>

<p> Simplify \(5x-13x+22x\).</p>
<p><strong>Solution<br></strong></p>
<p>All three terms are multiples of \(x\) and so are like terms.
The expression can be simplified to \(14x\).</p>
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<h4 class="HELM_example">Example</h4>
<p> Simplify \(5z+2x\).</p>
<p><strong>Solution<br></strong></p>
<p>\(5z\) and \(2x\) are not like terms. They are not
multiples of the same quantity. This expression cannot
 be simplified.</p>
<hr>
<h4 class="HELM_example">Example</h4>
<p> Simplify \(2x^2-7x+11x^2+x\).</p>
<p><strong>Solution<br></strong></p>
<p>\(2x^2\) and \(11x^2\), both being multiples of \(x^2\), can be
collected together and added to give \(13x^2\).</p>
<p>Similarly, \(-7x\) and \(x\)
 can be added to give \(-6x\).</p>
<p> We get
\(2x^2-7x+11x^2+x= 13x^2-6x
\) which cannot be simplified further.</p>
<hr>
<h4 class="HELM_example">Example</h4>
<p> Simplify \(3a^2b-7a^2b-2b^2+a^2\).</p>
<p><strong>Solution<br></strong></p>
<p>Note that \(3a^2b\) and \(7a^2b\) are both multiples
of \(a^2b\) and so are like terms. There are no other like terms.
Therefore</p>
<p>\(3a^2b-7a^2b-2b^2+a^2 = -4a^2b-2b^2+a^2\)</p>
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