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Activity Discussion Math Simplify

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  • Mawar Tanjung

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    October 1, 2024 at 12:55 pm
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    To simplify the expression <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mn>3</mn><mo stretchy=”false”>(</mo><mi>y</mi><mo>−</mo><mn>5</mn><mo stretchy=”false”>)</mo><mo>+</mo><mn>2</mn><mo stretchy=”false”>(</mo><mi>y</mi><mo>+</mo><mn>3</mn><mo stretchy=”false”>)</mo></mrow><annotation encoding=”application/x-tex”>3(y – 5) + 2(y + 3)</annotation></semantics></math>3(y−5)+2(y+3), follow these steps:

    1. Distribute <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mn>3</mn></mrow><annotation encoding=”application/x-tex”>3</annotation></semantics></math>3 and <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mn>2</mn></mrow><annotation encoding=”application/x-tex”>2</annotation></semantics></math>2 to the terms inside the parentheses:

      <math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mn>3</mn><mo stretchy=”false”>(</mo><mi>y</mi><mo>−</mo><mn>5</mn><mo stretchy=”false”>)</mo><mo>=</mo><mn>3</mn><mi>y</mi><mo>−</mo><mn>15</mn></mrow><annotation encoding=”application/x-tex”>3(y – 5) = 3y – 15</annotation></semantics></math>3(y−5)=3y−15
      <math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mn>2</mn><mo stretchy=”false”>(</mo><mi>y</mi><mo>+</mo><mn>3</mn><mo stretchy=”false”>)</mo><mo>=</mo><mn>2</mn><mi>y</mi><mo>+</mo><mn>6</mn></mrow><annotation encoding=”application/x-tex”>2(y + 3) = 2y + 6</annotation></semantics></math>2(y+3)=2y+6

    2. Combine the results:

      <math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mn>3</mn><mi>y</mi><mo>−</mo><mn>15</mn><mo>+</mo><mn>2</mn><mi>y</mi><mo>+</mo><mn>6</mn></mrow><annotation encoding=”application/x-tex”>3y – 15 + 2y + 6</annotation></semantics></math>3y−15+2y+6

    3. Combine like terms:

      <math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mo stretchy=”false”>(</mo><mn>3</mn><mi>y</mi><mo>+</mo><mn>2</mn><mi>y</mi><mo stretchy=”false”>)</mo><mo>+</mo><mo stretchy=”false”>(</mo><mo>−</mo><mn>15</mn><mo>+</mo><mn>6</mn><mo stretchy=”false”>)</mo><mo>=</mo><mn>5</mn><mi>y</mi><mo>−</mo><mn>9</mn></mrow><annotation encoding=”application/x-tex”>(3y + 2y) + (-15 + 6) = 5y – 9</annotation></semantics></math>(3y+2y)+(−15+6)=5y−9

    The simplified expression is:

    <math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><menclose notation=”box”><mstyle scriptlevel=”0″ displaystyle=”false”><mstyle scriptlevel=”0″ displaystyle=”false”><mstyle scriptlevel=”0″ displaystyle=”true”><mrow><mn>5</mn><mi>y</mi><mo>−</mo><mn>9</mn></mrow></mstyle></mstyle></mstyle></menclose></mrow><annotation encoding=”application/x-tex”>\boxed{5y – 9}</annotation></semantics></math>5y−9​

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