Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{red}{-2q^4}\color{blue}{-6})(\color{red}{2q^4}\color{blue}{-6})=\color{blue}{(-6)}^2-\color{red}{(2q^4)}^2=36-4q^{8}\)
2. \((\color{blue}{q}\color{red}{+2})(\color{blue}{q}\color{red}{-2})=\color{blue}{q}^2-\color{red}{2}^2=q^2-4\)
3. \((\color{red}{11y^3}\color{blue}{+14q})(\color{red}{-11y^3}\color{blue}{+14q})=\color{blue}{(14q)}^2-\color{red}{(11y^3)}^2=196q^2-121y^{6}\)
4. \((\color{red}{12q^4}\color{blue}{+6})(\color{red}{-12q^4}\color{blue}{+6})=\color{blue}{6}^2-\color{red}{(12q^4)}^2=36-144q^{8}\)
5. \((\color{red}{4p^3}\color{blue}{+8x})(\color{red}{-4p^3}\color{blue}{+8x})=\color{blue}{(8x)}^2-\color{red}{(4p^3)}^2=64x^2-16p^{6}\)
6. \((\color{blue}{b}\color{red}{-6})(\color{blue}{b}\color{red}{+6})=\color{blue}{b}^2-\color{red}{6}^2=b^2-36\)
7. \((\color{blue}{-2q}\color{red}{-6})(\color{blue}{-2q}\color{red}{+6})=\color{blue}{(-2q)}^2-\color{red}{(-6)}^2=4q^2-36\)
8. \((-8p^4-3s)^2=(-8p^4)^2\color{magenta}{+2.(-8p^4).(-3s)}+(-3s)^2=64p^{8}\color{magenta}{+48p^4s}+9s^2\)
9. \((\color{red}{12a^3}\color{blue}{-8p})(\color{red}{-12a^3}\color{blue}{-8p})=\color{blue}{(-8p)}^2-\color{red}{(12a^3)}^2=64p^2-144a^{6}\)
10. \((-13s-11)(-13s-11)=(-13s-11)^2=(-13s)^2+\color{magenta}{2.(-13s).(-11)}+(-11)^2=169s^2\color{magenta}{+286s}+121\)
11. \((\color{blue}{-11y}\color{red}{+1})(\color{blue}{-11y}\color{red}{-1})=\color{blue}{(-11y)}^2-\color{red}{(1)}^2=121y^2-1\)
12. \((q-13)(q-13)=(q-13)^2=q^2+\color{magenta}{2.q.(-13)}+(-13)^2=q^2\color{magenta}{-26q}+169\)