Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((-3x^3+7b)(-3x^3+7b)=(-3x^3+7b)^2=(-3x^3)^2\color{magenta}{+2.(-3x^3).(7b)}+(7b)^2=9x^{6}\color{magenta}{-42bx^3}+49b^2\)
2. \((x-1)(x-1)=(x-1)^2=x^2+\color{magenta}{2.x.(-1)}+(-1)^2=x^2\color{magenta}{-2x}+1\)
3. \((x+2)(x+2)=(x+2)^2=x^2+\color{magenta}{2.x.2}+2^2=x^2\color{magenta}{+4x}+4\)
4. \((\color{red}{-12a^5}\color{blue}{-1})(\color{red}{12a^5}\color{blue}{-1})=\color{blue}{(-1)}^2-\color{red}{(12a^5)}^2=1-144a^{10}\)
5. \((\color{red}{15p^5}\color{blue}{+16b})(\color{red}{-15p^5}\color{blue}{+16b})=\color{blue}{(16b)}^2-\color{red}{(15p^5)}^2=256b^2-225p^{10}\)
6. \((q^3-6x)^2=(q^3)^2\color{magenta}{+2.(q^3).(-6x)}+(-6x)^2=q^{6}\color{magenta}{-12q^3x}+36x^2\)
7. \((-8a^2-16p)^2=(-8a^2)^2\color{magenta}{+2.(-8a^2).(-16p)}+(-16p)^2=64a^{4}\color{magenta}{+256a^2p}+256p^2\)
8. \((9s^2+y)(9s^2+y)=(9s^2+y)^2=(9s^2)^2\color{magenta}{+2.(9s^2).(y)}+(y)^2=81s^{4}\color{magenta}{+18s^2y}+1y^2\)
9. \((y-6)(y-6)=(y-6)^2=y^2+\color{magenta}{2.y.(-6)}+(-6)^2=y^2\color{magenta}{-12y}+36\)
10. \((12a^2+7q)^2=(12a^2)^2\color{magenta}{+2.(12a^2).(7q)}+(7q)^2=144a^{4}\color{magenta}{+168a^2q}+49q^2\)
11. \((\color{red}{-13q}\color{blue}{-14})(\color{red}{13q}\color{blue}{-14})=\color{blue}{(-14)}^2-\color{red}{(13q)}^2=196-169q^2\)
12. \((\color{blue}{10y}\color{red}{-16})(\color{blue}{10y}\color{red}{+16})=\color{blue}{(10y)}^2-\color{red}{(-16)}^2=100y^2-256\)