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Q.1. Find the following products;

  1.     \left(y+9\right)\left(y-9\right)=y^2-81    
  2.     \left(4+b\right)\left(4-b\right)=16-b^2    
  3.     \left(3x-5\right)\left(3x+5\right)=9x^2-25    
  4.     \left(a-\frac{2}{3}\right)\left(a+\frac{2}{3}\right)=a^2-\frac{4}{9}    

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Q2. Find the following products;

  1.     \left(3x-5\right)\left(3x+5\right)=9x^2-25    
  2.     \left(2+7x\right)\left(2-7x\right)=4-49x^2    
  3.     \left(\frac{a}{2}+3\right)\left(\frac{a}{2}-3\right)=\frac{a^2}{4}-9    
  4.     \left(4x+3y\right)\left(4x-3y\right)=16x^2-9y^2    

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Q.3. Find the following products;

  1.     \left(\frac{a}{3}-\frac{b}{4}\right)\left(\frac{a}{3}+\frac{b}{4}\right)=\frac{a^2}{9}-\frac{b^2}{16}    
  2.     \left(\frac{t}{2}-\frac{1}{3}\right)\left(\frac{t}{2}+\frac{1}{3}\right)=\frac{t^2}{4}-\frac{1}{9}    

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Q.4. Find the following products;

  1.     \left(\frac{2}{x}+\frac{3}{y}\right)\left(\frac{2}{x}-\frac{3}{y}\right)=\frac{4}{x^2}-\frac{9}{y^2}    
  2.     \left(\frac{1}{a}-\frac{1}{b}\right)\left(\frac{1}{a}+\frac{1}{b}\right)=\frac{1}{a^2}-\frac{1}{b^2}    
  3.     \left(\frac{1}{3x}+\frac{2}{5y}\right)\left(\frac{1}{3x}-\frac{2}{5y}\right)=\frac{1}{9x^2}-\frac{2}{25y^2}    
  4.     \left(1.1x-0.3y\right)\left(1.1x+0.3y\right)=1.21x^2-0.09y^2    

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Q.5. Find the following products;

  1.     \left(a^2+2b^2\right)\left(a^2-2b^2\right)=a^4-4b^4    
  2.     \left(6x^2-7y^2\right)\left(6x^2+7y^2\right)=36x^4-49y^4    
  3.     \left(4x^2+2yz\right)\left(2x^2-yz\right)=8x^4+4x^2yz-4x^2yz-2y^2z^2=\ 8x^4-2y^2z^2    
  4.     \left(ab-\frac{3}{2}cd\right)\left(2ab+3cd\right)=2a^2b^2-3abcd+3abcd-\frac{9}{2}c^2d^2=2a^2b^2-\frac{9}{2}c^2d^2    

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Q6. Find the following products;

    \left(2x+3\right)\left(2x-3\right)\left(4x^2+9\right)    

    =\ \left(4x^2-9\right)\left(4x^2+9\right)    

    =\ 16x^2-81    

    \\     

    \left(x+2y\right)\left(x-2y\right)\left(x^2+4y^2\right)    

    =\ \left(x^2-4y^2\right)\left(x^2+4y^2\right)    

    =\ x^4-16y^4    

    \\     

    \left(a+bc\right)\left(a-bc\right)\left(a^2+b^2c^2\right)    

    =\ \left(a^2-b^2c^2\right)\left(a^2+b^2c^2\right)    

    ={\ a}^4-b^4c^4    

    \\     

    \left(\frac{2}{5}+x\right)\left(\frac{2}{5}-x\right)\left(\frac{4}{25}+x^2\right)    

    =\ \left(\frac{4}{25}-x^2\right)\left(\frac{4}{25}+x^2\right)    

    =\ \frac{16}{625}-x^4    

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Q7. Using the identity     \left(a+b\right)\left(a-b\right)=\left(a^2-b^2\right)   evaluate the following.

  1.     88\times{}112=\left(100-12\right)\left(100+12\right)=1000-144=9856    
  2.     153\times{}167=\left(160-7\right)\left(160+7\right)=25600-49=25551    
  3.     10.8\times{}9.2=\left(10+0.8\right)\left(10-0.8\right)={10}^2-{0.8}^2=100-0.64=99.36    
  4.     3\frac{1}{3}\times{}4\frac{2}{3}=\left(4-\frac{2}{3}\right)\left(4+\frac{2}{3}\right)=16-\frac{4}{9}=15\frac{5}{9}    
  5.     9\frac{1}{4}\times{}15\frac{3}{4}=\left(\frac{25}{2}-3\frac{1}{4}\right)\left(\frac{25}{2}+3\frac{1}{4}\right)=145.6875    
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