Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((a-10)^2=a^2+\color{magenta}{2.a.(-10)}+(-10)^2=a^2\color{magenta}{-20a}+100\)
2. \((\color{red}{-7b^3}\color{blue}{+6s})(\color{red}{7b^3}\color{blue}{+6s})=\color{blue}{(6s)}^2-\color{red}{(7b^3)}^2=36s^2-49b^{6}\)
3. \((-9p^5-2s)(-9p^5-2s)=(-9p^5-2s)^2=(-9p^5)^2\color{magenta}{+2.(-9p^5).(-2s)}+(-2s)^2=81p^{10}\color{magenta}{+36p^5s}+4s^2\)
4. \((\color{blue}{-9p}\color{red}{+5})(\color{blue}{-9p}\color{red}{-5})=\color{blue}{(-9p)}^2-\color{red}{(5)}^2=81p^2-25\)
5. \((\color{blue}{b}\color{red}{+2})(\color{blue}{b}\color{red}{-2})=\color{blue}{b}^2-\color{red}{2}^2=b^2-4\)
6. \((-2q^2+9x)(-2q^2+9x)=(-2q^2+9x)^2=(-2q^2)^2\color{magenta}{+2.(-2q^2).(9x)}+(9x)^2=4q^{4}\color{magenta}{-36q^2x}+81x^2\)
7. \((\color{red}{2a^2}\color{blue}{+12})(\color{red}{-2a^2}\color{blue}{+12})=\color{blue}{12}^2-\color{red}{(2a^2)}^2=144-4a^{4}\)
8. \((-7b-5)(-7b-5)=(-7b-5)^2=(-7b)^2+\color{magenta}{2.(-7b).(-5)}+(-5)^2=49b^2\color{magenta}{+70b}+25\)
9. \((\color{red}{-7y}\color{blue}{-15})(\color{red}{7y}\color{blue}{-15})=\color{blue}{(-15)}^2-\color{red}{(7y)}^2=225-49y^2\)
10. \((\color{blue}{10b}\color{red}{-5})(\color{blue}{10b}\color{red}{+5})=\color{blue}{(10b)}^2-\color{red}{(-5)}^2=100b^2-25\)
11. \((\color{red}{6x^4}\color{blue}{-6s})(\color{red}{-6x^4}\color{blue}{-6s})=\color{blue}{(-6s)}^2-\color{red}{(6x^4)}^2=36s^2-36x^{8}\)
12. \((-4b+14)^2=(-4b)^2+\color{magenta}{2.(-4b).14}+14^2=16b^2\color{magenta}{-112b}+196\)