Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{blue}{p}\color{red}{-6})(\color{blue}{p}\color{red}{+6})=\color{blue}{p}^2-\color{red}{6}^2=p^2-36\)
2. \((13p^4-14)(13p^4-14)=(13p^4-14)^2=(13p^4)^2\color{magenta}{+2.(13p^4).(-14)}+(-14)^2=169p^{8}\color{magenta}{-364p^4}+196\)
3. \((2q-9)(2q-9)=(2q-9)^2=(2q)^2+\color{magenta}{2.(2q).(-9)}+(-9)^2=4q^2\color{magenta}{-36q}+81\)
4. \((y-5)(y-5)=(y-5)^2=y^2+\color{magenta}{2.y.(-5)}+(-5)^2=y^2\color{magenta}{-10y}+25\)
5. \((\color{blue}{b}\color{red}{-1})(\color{blue}{b}\color{red}{+1})=\color{blue}{b}^2-\color{red}{1}^2=b^2-1\)
6. \((\color{blue}{12p^3}\color{red}{+16x})(\color{blue}{12p^3}\color{red}{-16x})=\color{blue}{(12p^3)}^2-\color{red}{(16x)}^2=144p^{6}-256x^2\)
7. \((q-10)(q-10)=(q-10)^2=q^2+\color{magenta}{2.q.(-10)}+(-10)^2=q^2\color{magenta}{-20q}+100\)
8. \((\color{red}{8s}\color{blue}{+14})(\color{red}{-8s}\color{blue}{+14})=\color{blue}{14}^2-\color{red}{(8s)}^2=196-64s^2\)
9. \((\color{blue}{-13p^4}\color{red}{-16})(\color{blue}{-13p^4}\color{red}{+16})=\color{blue}{(-13p^4)}^2-\color{red}{(-16)}^2=169p^{8}-256\)
10. \((-4p-10)^2=(-4p)^2+\color{magenta}{2.(-4p).(-10)}+(-10)^2=16p^2\color{magenta}{+80p}+100\)
11. \((x-12)^2=x^2+\color{magenta}{2.x.(-12)}+(-12)^2=x^2\color{magenta}{-24x}+144\)
12. \((\color{blue}{-14y}\color{red}{+1})(\color{blue}{-14y}\color{red}{-1})=\color{blue}{(-14y)}^2-\color{red}{(1)}^2=196y^2-1\)