Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{blue}{8s^3}\color{red}{+3x})(\color{blue}{8s^3}\color{red}{-3x})=\color{blue}{(8s^3)}^2-\color{red}{(3x)}^2=64s^{6}-9x^2\)
2. \((-5x^3-1)^2=(-5x^3)^2\color{magenta}{+2.(-5x^3).(-1)}+(-1)^2=25x^{6}\color{magenta}{+10x^3}+1\)
3. \((y+14)^2=y^2+\color{magenta}{2.y.14}+14^2=y^2\color{magenta}{+28y}+196\)
4. \((-10a+1)^2=(-10a)^2+\color{magenta}{2.(-10a).1}+1^2=100a^2\color{magenta}{-20a}+1\)
5. \((\color{red}{-14q^2}\color{blue}{+8})(\color{red}{14q^2}\color{blue}{+8})=\color{blue}{8}^2-\color{red}{(14q^2)}^2=64-196q^{4}\)
6. \((\color{blue}{x}\color{red}{-14})(\color{blue}{x}\color{red}{+14})=\color{blue}{(x)}^2-\color{red}{(-14)}^2=x^2-196\)
7. \((\color{blue}{-8b}\color{red}{-10})(\color{blue}{-8b}\color{red}{+10})=\color{blue}{(-8b)}^2-\color{red}{(-10)}^2=64b^2-100\)
8. \((-15x^5-14)(-15x^5-14)=(-15x^5-14)^2=(-15x^5)^2\color{magenta}{+2.(-15x^5).(-14)}+(-14)^2=225x^{10}\color{magenta}{+420x^5}+196\)
9. \((\color{blue}{q}\color{red}{-1})(\color{blue}{q}\color{red}{+1})=\color{blue}{q}^2-\color{red}{1}^2=q^2-1\)
10. \((\color{blue}{-15b}\color{red}{-4})(\color{blue}{-15b}\color{red}{+4})=\color{blue}{(-15b)}^2-\color{red}{(-4)}^2=225b^2-16\)
11. \((14q^3-7)^2=(14q^3)^2\color{magenta}{+2.(14q^3).(-7)}+(-7)^2=196q^{6}\color{magenta}{-196q^3}+49\)
12. \((\color{red}{5p^3}\color{blue}{+10})(\color{red}{-5p^3}\color{blue}{+10})=\color{blue}{10}^2-\color{red}{(5p^3)}^2=100-25p^{6}\)