Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((14p-6)(14p-6)=(14p-6)^2=(14p)^2+\color{magenta}{2.(14p).(-6)}+(-6)^2=196p^2\color{magenta}{-168p}+36\)
2. \((\color{blue}{3b}\color{red}{-2})(\color{blue}{3b}\color{red}{+2})=\color{blue}{(3b)}^2-\color{red}{(-2)}^2=9b^2-4\)
3. \((-6x-2)(-6x-2)=(-6x-2)^2=(-6x)^2+\color{magenta}{2.(-6x).(-2)}+(-2)^2=36x^2\color{magenta}{+24x}+4\)
4. \((-6a^2+14b)^2=(-6a^2)^2\color{magenta}{+2.(-6a^2).(14b)}+(14b)^2=36a^{4}\color{magenta}{-168a^2b}+196b^2\)
5. \((\color{red}{-3s^5}\color{blue}{+5x})(\color{red}{3s^5}\color{blue}{+5x})=\color{blue}{(5x)}^2-\color{red}{(3s^5)}^2=25x^2-9s^{10}\)
6. \((-8b^3+2y)(-8b^3+2y)=(-8b^3+2y)^2=(-8b^3)^2\color{magenta}{+2.(-8b^3).(2y)}+(2y)^2=64b^{6}\color{magenta}{-32b^3y}+4y^2\)
7. \((-15x^5-10q)^2=(-15x^5)^2\color{magenta}{+2.(-15x^5).(-10q)}+(-10q)^2=225x^{10}\color{magenta}{+300qx^5}+100q^2\)
8. \((\color{blue}{3p}\color{red}{+7})(\color{blue}{3p}\color{red}{-7})=\color{blue}{(3p)}^2-\color{red}{(7)}^2=9p^2-49\)
9. \((\color{blue}{q}\color{red}{-15})(\color{blue}{q}\color{red}{+15})=\color{blue}{q}^2-\color{red}{15}^2=q^2-225\)
10. \((\color{blue}{p}\color{red}{-4})(\color{blue}{p}\color{red}{+4})=\color{blue}{p}^2-\color{red}{4}^2=p^2-16\)
11. \((s-10)(s-10)=(s-10)^2=s^2+\color{magenta}{2.s.(-10)}+(-10)^2=s^2\color{magenta}{-20s}+100\)
12. \((12s^5-9y)(12s^5-9y)=(12s^5-9y)^2=(12s^5)^2\color{magenta}{+2.(12s^5).(-9y)}+(-9y)^2=144s^{10}\color{magenta}{-216s^5y}+81y^2\)