Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

1. \((-4x^2-14p)(-4x^2-14p)\)
2. \((9y-9)(-9y-9)\)
3. \((y^2+4)^2\)
4. \((11p-4)^2\)
5. \((14x^5+6a)(-14x^5+6a)\)
6. \((p-9)(p+9)\)
7. \((-7p^4+4q)(7p^4+4q)\)
8. \((16s^5+13x)^2\)
9. \((a-14)^2\)
10. \((q+15)(q-15)\)
11. \((11s^3-1)(-11s^3-1)\)
12. \((-13y^2-14)(13y^2-14)\)

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((-4x^2-14p)(-4x^2-14p)=(-4x^2-14p)^2=(-4x^2)^2\color{magenta}{+2.(-4x^2).(-14p)}+(-14p)^2=16x^{4}\color{magenta}{+112px^2}+196p^2\)
2. \((\color{red}{9y}\color{blue}{-9})(\color{red}{-9y}\color{blue}{-9})=\color{blue}{(-9)}^2-\color{red}{(9y)}^2=81-81y^2\)
3. \((y^2+4)^2=(y^2)^2\color{magenta}{+2.(y^2).4}+4^2=1y^{4}\color{magenta}{+8y^2}+16\)
4. \((11p-4)^2=(11p)^2+\color{magenta}{2.(11p).(-4)}+(-4)^2=121p^2\color{magenta}{-88p}+16\)
5. \((\color{red}{14x^5}\color{blue}{+6a})(\color{red}{-14x^5}\color{blue}{+6a})=\color{blue}{(6a)}^2-\color{red}{(14x^5)}^2=36a^2-196x^{10}\)
6. \((\color{blue}{p}\color{red}{-9})(\color{blue}{p}\color{red}{+9})=\color{blue}{p}^2-\color{red}{9}^2=p^2-81\)
7. \((\color{red}{-7p^4}\color{blue}{+4q})(\color{red}{7p^4}\color{blue}{+4q})=\color{blue}{(4q)}^2-\color{red}{(7p^4)}^2=16q^2-49p^{8}\)
8. \((16s^5+13x)^2=(16s^5)^2\color{magenta}{+2.(16s^5).(13x)}+(13x)^2=256s^{10}\color{magenta}{+416s^5x}+169x^2\)
9. \((a-14)^2=a^2+\color{magenta}{2.a.(-14)}+(-14)^2=a^2\color{magenta}{-28a}+196\)
10. \((\color{blue}{q}\color{red}{+15})(\color{blue}{q}\color{red}{-15})=\color{blue}{q}^2-\color{red}{15}^2=q^2-225\)
11. \((\color{red}{11s^3}\color{blue}{-1})(\color{red}{-11s^3}\color{blue}{-1})=\color{blue}{(-1)}^2-\color{red}{(11s^3)}^2=1-121s^{6}\)
12. \((\color{red}{-13y^2}\color{blue}{-14})(\color{red}{13y^2}\color{blue}{-14})=\color{blue}{(-14)}^2-\color{red}{(13y^2)}^2=196-169y^{4}\)