Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((5s^4-12a)^2=(5s^4)^2\color{magenta}{+2.(5s^4).(-12a)}+(-12a)^2=25s^{8}\color{magenta}{-120as^4}+144a^2\)
2. \((\color{red}{6y}\color{blue}{+13})(\color{red}{-6y}\color{blue}{+13})=\color{blue}{13}^2-\color{red}{(6y)}^2=169-36y^2\)
3. \((\color{red}{-5q^5}\color{blue}{-7})(\color{red}{5q^5}\color{blue}{-7})=\color{blue}{(-7)}^2-\color{red}{(5q^5)}^2=49-25q^{10}\)
4. \((x+5)(x+5)=(x+5)^2=x^2+\color{magenta}{2.x.5}+5^2=x^2\color{magenta}{+10x}+25\)
5. \((14s-6)(14s-6)=(14s-6)^2=(14s)^2+\color{magenta}{2.(14s).(-6)}+(-6)^2=196s^2\color{magenta}{-168s}+36\)
6. \((\color{blue}{-7x^2}\color{red}{+15})(\color{blue}{-7x^2}\color{red}{-15})=\color{blue}{(-7x^2)}^2-\color{red}{15}^2=49x^{4}-225\)
7. \((\color{blue}{-6y^2}\color{red}{-7})(\color{blue}{-6y^2}\color{red}{+7})=\color{blue}{(-6y^2)}^2-\color{red}{(-7)}^2=36y^{4}-49\)
8. \((\color{red}{15a^2}\color{blue}{-9})(\color{red}{-15a^2}\color{blue}{-9})=\color{blue}{(-9)}^2-\color{red}{(15a^2)}^2=81-225a^{4}\)
9. \((\color{red}{-7s^2}\color{blue}{+6})(\color{red}{7s^2}\color{blue}{+6})=\color{blue}{6}^2-\color{red}{(7s^2)}^2=36-49s^{4}\)
10. \((\color{blue}{10b^3}\color{red}{+11p})(\color{blue}{10b^3}\color{red}{-11p})=\color{blue}{(10b^3)}^2-\color{red}{(11p)}^2=100b^{6}-121p^2\)
11. \((\color{blue}{y}\color{red}{+1})(\color{blue}{y}\color{red}{-1})=\color{blue}{y}^2-\color{red}{1}^2=y^2-1\)
12. \((y-3)^2=y^2+\color{magenta}{2.y.(-3)}+(-3)^2=y^2\color{magenta}{-6y}+9\)