Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((-3b^3+6)(-3b^3+6)=(-3b^3+6)^2=(-3b^3)^2\color{magenta}{+2.(-3b^3).6}+6^2=9b^{6}\color{magenta}{-36b^3}+36\)
2. \((\color{blue}{b}\color{red}{-4})(\color{blue}{b}\color{red}{+4})=\color{blue}{b}^2-\color{red}{4}^2=b^2-16\)
3. \((\color{blue}{-2q^5}\color{red}{+1})(\color{blue}{-2q^5}\color{red}{-1})=\color{blue}{(-2q^5)}^2-\color{red}{1}^2=4q^{10}-1\)
4. \((\color{blue}{a}\color{red}{+2})(\color{blue}{a}\color{red}{-2})=\color{blue}{a}^2-\color{red}{2}^2=a^2-4\)
5. \((\color{blue}{a^4}\color{red}{+8})(\color{blue}{a^4}\color{red}{-8})=\color{blue}{(a^4)}^2-\color{red}{8}^2=a^{8}-64\)
6. \((s+14)(s+14)=(s+14)^2=s^2+\color{magenta}{2.s.14}+14^2=s^2\color{magenta}{+28s}+196\)
7. \((-6a^5-13)^2=(-6a^5)^2\color{magenta}{+2.(-6a^5).(-13)}+(-13)^2=36a^{10}\color{magenta}{+156a^5}+169\)
8. \((10x^5-11)^2=(10x^5)^2\color{magenta}{+2.(10x^5).(-11)}+(-11)^2=100x^{10}\color{magenta}{-220x^5}+121\)
9. \((\color{red}{5x}\color{blue}{+5})(\color{red}{-5x}\color{blue}{+5})=\color{blue}{5}^2-\color{red}{(5x)}^2=25-25x^2\)
10. \((-4q^5+10)^2=(-4q^5)^2\color{magenta}{+2.(-4q^5).10}+10^2=16q^{10}\color{magenta}{-80q^5}+100\)
11. \((-x^4+12)^2=(-x^4)^2\color{magenta}{+2.(-x^4).12}+12^2=1x^{8}\color{magenta}{-24x^4}+144\)
12. \((\color{blue}{-4y^4}\color{red}{+8})(\color{blue}{-4y^4}\color{red}{-8})=\color{blue}{(-4y^4)}^2-\color{red}{8}^2=16y^{8}-64\)