Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

1. \((12q^3-6x)(12q^3+6x)\)
2. \((14b^4-13)(-14b^4-13)\)
3. \((7y+10)(-7y+10)\)
4. \((-3y-13)^2\)
5. \((5s^5-5q)(5s^5+5q)\)
6. \((13p+16)(-13p+16)\)
7. \((b-9)^2\)
8. \((2s^2-11p)(-2s^2-11p)\)
9. \((12a^3-b)(12a^3+b)\)
10. \((s-15)(s+15)\)
11. \((-6b^2+6x)(-6b^2+6x)\)
12. \((q+14)(q-14)\)

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{blue}{12q^3}\color{red}{-6x})(\color{blue}{12q^3}\color{red}{+6x})=\color{blue}{(12q^3)}^2-\color{red}{(-6x)}^2=144q^{6}-36x^2\)
2. \((\color{red}{14b^4}\color{blue}{-13})(\color{red}{-14b^4}\color{blue}{-13})=\color{blue}{(-13)}^2-\color{red}{(14b^4)}^2=169-196b^{8}\)
3. \((\color{red}{7y}\color{blue}{+10})(\color{red}{-7y}\color{blue}{+10})=\color{blue}{10}^2-\color{red}{(7y)}^2=100-49y^2\)
4. \((-3y-13)^2=(-3y)^2+\color{magenta}{2.(-3y).(-13)}+(-13)^2=9y^2\color{magenta}{+78y}+169\)
5. \((\color{blue}{5s^5}\color{red}{-5q})(\color{blue}{5s^5}\color{red}{+5q})=\color{blue}{(5s^5)}^2-\color{red}{(-5q)}^2=25s^{10}-25q^2\)
6. \((\color{red}{13p}\color{blue}{+16})(\color{red}{-13p}\color{blue}{+16})=\color{blue}{16}^2-\color{red}{(13p)}^2=256-169p^2\)
7. \((b-9)^2=b^2+\color{magenta}{2.b.(-9)}+(-9)^2=b^2\color{magenta}{-18b}+81\)
8. \((\color{red}{2s^2}\color{blue}{-11p})(\color{red}{-2s^2}\color{blue}{-11p})=\color{blue}{(-11p)}^2-\color{red}{(2s^2)}^2=121p^2-4s^{4}\)
9. \((\color{blue}{12a^3}\color{red}{-b})(\color{blue}{12a^3}\color{red}{+b})=\color{blue}{(12a^3)}^2-\color{red}{(-1b)}^2=144a^{6}-1b^2\)
10. \((\color{blue}{s}\color{red}{-15})(\color{blue}{s}\color{red}{+15})=\color{blue}{s}^2-\color{red}{15}^2=s^2-225\)
11. \((-6b^2+6x)(-6b^2+6x)=(-6b^2+6x)^2=(-6b^2)^2\color{magenta}{+2.(-6b^2).(6x)}+(6x)^2=36b^{4}\color{magenta}{-72b^2x}+36x^2\)
12. \((\color{blue}{q}\color{red}{+14})(\color{blue}{q}\color{red}{-14})=\color{blue}{q}^2-\color{red}{14}^2=q^2-196\)