Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{blue}{p}\color{red}{-15})(\color{blue}{p}\color{red}{+15})=\color{blue}{p}^2-\color{red}{15}^2=p^2-225\)
2. \((p-15)^2=p^2+\color{magenta}{2.p.(-15)}+(-15)^2=p^2\color{magenta}{-30p}+225\)
3. \((b-10)(b-10)=(b-10)^2=b^2+\color{magenta}{2.b.(-10)}+(-10)^2=b^2\color{magenta}{-20b}+100\)
4. \((\color{red}{4b}\color{blue}{-5})(\color{red}{-4b}\color{blue}{-5})=\color{blue}{(-5)}^2-\color{red}{(4b)}^2=25-16b^2\)
5. \((\color{blue}{y}\color{red}{+13})(\color{blue}{y}\color{red}{-13})=\color{blue}{y}^2-\color{red}{13}^2=y^2-169\)
6. \((\color{blue}{-11x^4}\color{red}{-13})(\color{blue}{-11x^4}\color{red}{+13})=\color{blue}{(-11x^4)}^2-\color{red}{(-13)}^2=121x^{8}-169\)
7. \((\color{red}{-3x^5}\color{blue}{+1})(\color{red}{3x^5}\color{blue}{+1})=\color{blue}{1}^2-\color{red}{(3x^5)}^2=1-9x^{10}\)
8. \((15x^3-12q)(15x^3-12q)=(15x^3-12q)^2=(15x^3)^2\color{magenta}{+2.(15x^3).(-12q)}+(-12q)^2=225x^{6}\color{magenta}{-360qx^3}+144q^2\)
9. \((\color{red}{-2p^3}\color{blue}{+15})(\color{red}{2p^3}\color{blue}{+15})=\color{blue}{15}^2-\color{red}{(2p^3)}^2=225-4p^{6}\)
10. \((\color{blue}{y^3}\color{red}{+3p})(\color{blue}{y^3}\color{red}{-3p})=\color{blue}{(y^3)}^2-\color{red}{(3p)}^2=y^{6}-9p^2\)
11. \((\color{blue}{-9y^5}\color{red}{-6})(\color{blue}{-9y^5}\color{red}{+6})=\color{blue}{(-9y^5)}^2-\color{red}{(-6)}^2=81y^{10}-36\)
12. \((y-8)^2=y^2+\color{magenta}{2.y.(-8)}+(-8)^2=y^2\color{magenta}{-16y}+64\)