Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

1. \((4b^5+2)(4b^5-2)\)
2. \((p-4)(p+4)\)
3. \((p+13)(p-13)\)
4. \((x+14)(x-14)\)
5. \((-16b^4+4a)(-16b^4+4a)\)
6. \((14s-9)(14s+9)\)
7. \((3x+1)(-3x+1)\)
8. \((4s^5-5)(-4s^5-5)\)
9. \((7s^5-13b)^2\)
10. \((x-2)^2\)
11. \((2s^3+5q)(2s^3-5q)\)
12. \((2a^3-4s)(2a^3+4s)\)

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{blue}{4b^5}\color{red}{+2})(\color{blue}{4b^5}\color{red}{-2})=\color{blue}{(4b^5)}^2-\color{red}{2}^2=16b^{10}-4\)
2. \((\color{blue}{p}\color{red}{-4})(\color{blue}{p}\color{red}{+4})=\color{blue}{p}^2-\color{red}{4}^2=p^2-16\)
3. \((\color{blue}{p}\color{red}{+13})(\color{blue}{p}\color{red}{-13})=\color{blue}{p}^2-\color{red}{13}^2=p^2-169\)
4. \((\color{blue}{x}\color{red}{+14})(\color{blue}{x}\color{red}{-14})=\color{blue}{x}^2-\color{red}{14}^2=x^2-196\)
5. \((-16b^4+4a)(-16b^4+4a)=(-16b^4+4a)^2=(-16b^4)^2\color{magenta}{+2.(-16b^4).(4a)}+(4a)^2=256b^{8}\color{magenta}{-128ab^4}+16a^2\)
6. \((\color{blue}{14s}\color{red}{-9})(\color{blue}{14s}\color{red}{+9})=\color{blue}{(14s)}^2-\color{red}{(-9)}^2=196s^2-81\)
7. \((\color{red}{3x}\color{blue}{+1})(\color{red}{-3x}\color{blue}{+1})=\color{blue}{1}^2-\color{red}{(3x)}^2=1-9x^2\)
8. \((\color{red}{4s^5}\color{blue}{-5})(\color{red}{-4s^5}\color{blue}{-5})=\color{blue}{(-5)}^2-\color{red}{(4s^5)}^2=25-16s^{10}\)
9. \((7s^5-13b)^2=(7s^5)^2\color{magenta}{+2.(7s^5).(-13b)}+(-13b)^2=49s^{10}\color{magenta}{-182bs^5}+169b^2\)
10. \((x-2)^2=x^2+\color{magenta}{2.x.(-2)}+(-2)^2=x^2\color{magenta}{-4x}+4\)
11. \((\color{blue}{2s^3}\color{red}{+5q})(\color{blue}{2s^3}\color{red}{-5q})=\color{blue}{(2s^3)}^2-\color{red}{(5q)}^2=4s^{6}-25q^2\)
12. \((\color{blue}{2a^3}\color{red}{-4s})(\color{blue}{2a^3}\color{red}{+4s})=\color{blue}{(2a^3)}^2-\color{red}{(-4s)}^2=4a^{6}-16s^2\)