Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((-p-12)^2=(-p)^2+\color{magenta}{2.(-p).(-12)}+(-12)^2=p^2\color{magenta}{+24p}+144\)
2. \((\color{blue}{11q}\color{red}{+6})(\color{blue}{11q}\color{red}{-6})=\color{blue}{(11q)}^2-\color{red}{(6)}^2=121q^2-36\)
3. \((-14x^3+16y)(-14x^3+16y)=(-14x^3+16y)^2=(-14x^3)^2\color{magenta}{+2.(-14x^3).(16y)}+(16y)^2=196x^{6}\color{magenta}{-448x^3y}+256y^2\)
4. \((-5x+5)(-5x+5)=(-5x+5)^2=(-5x)^2+\color{magenta}{2.(-5x).5}+5^2=25x^2\color{magenta}{-50x}+25\)
5. \((-12a-16)^2=(-12a)^2+\color{magenta}{2.(-12a).(-16)}+(-16)^2=144a^2\color{magenta}{+384a}+256\)
6. \((-14x^2+4)(-14x^2+4)=(-14x^2+4)^2=(-14x^2)^2\color{magenta}{+2.(-14x^2).4}+4^2=196x^{4}\color{magenta}{-112x^2}+16\)
7. \((\color{red}{-11x^4}\color{blue}{+7})(\color{red}{11x^4}\color{blue}{+7})=\color{blue}{7}^2-\color{red}{(11x^4)}^2=49-121x^{8}\)
8. \((y^3-3)(y^3-3)=(y^3-3)^2=(y^3)^2\color{magenta}{+2.(y^3).(-3)}+(-3)^2=1y^{6}\color{magenta}{-6y^3}+9\)
9. \((\color{blue}{-3p^4}\color{red}{+7y})(\color{blue}{-3p^4}\color{red}{-7y})=\color{blue}{(-3p^4)}^2-\color{red}{(7y)}^2=9p^{8}-49y^2\)
10. \((q-14)^2=q^2+\color{magenta}{2.q.(-14)}+(-14)^2=q^2\color{magenta}{-28q}+196\)
11. \((-7x^2-14)(-7x^2-14)=(-7x^2-14)^2=(-7x^2)^2\color{magenta}{+2.(-7x^2).(-14)}+(-14)^2=49x^{4}\color{magenta}{+196x^2}+196\)
12. \((\color{blue}{y}\color{red}{+14})(\color{blue}{y}\color{red}{-14})=\color{blue}{y}^2-\color{red}{14}^2=y^2-196\)