Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{blue}{-9y^2}\color{red}{+15})(\color{blue}{-9y^2}\color{red}{-15})=\color{blue}{(-9y^2)}^2-\color{red}{15}^2=81y^{4}-225\)
2. \((-12a^2-13)(-12a^2-13)=(-12a^2-13)^2=(-12a^2)^2\color{magenta}{+2.(-12a^2).(-13)}+(-13)^2=144a^{4}\color{magenta}{+312a^2}+169\)
3. \((-6s+9)^2=(-6s)^2+\color{magenta}{2.(-6s).9}+9^2=36s^2\color{magenta}{-108s}+81\)
4. \((\color{blue}{-8p^5}\color{red}{+16})(\color{blue}{-8p^5}\color{red}{-16})=\color{blue}{(-8p^5)}^2-\color{red}{16}^2=64p^{10}-256\)
5. \((\color{red}{-5x^2}\color{blue}{+16a})(\color{red}{5x^2}\color{blue}{+16a})=\color{blue}{(16a)}^2-\color{red}{(5x^2)}^2=256a^2-25x^{4}\)
6. \((10p^5-15y)(10p^5-15y)=(10p^5-15y)^2=(10p^5)^2\color{magenta}{+2.(10p^5).(-15y)}+(-15y)^2=100p^{10}\color{magenta}{-300p^5y}+225y^2\)
7. \((s+1)(s+1)=(s+1)^2=(s)^2+\color{magenta}{2.(s).1}+1^2=s^2\color{magenta}{+2s}+1\)
8. \((16s^2+13)^2=(16s^2)^2\color{magenta}{+2.(16s^2).13}+13^2=256s^{4}\color{magenta}{+416s^2}+169\)
9. \((\color{blue}{a}\color{red}{+2})(\color{blue}{a}\color{red}{-2})=\color{blue}{a}^2-\color{red}{2}^2=a^2-4\)
10. \((\color{red}{-16q^2}\color{blue}{-4})(\color{red}{16q^2}\color{blue}{-4})=\color{blue}{(-4)}^2-\color{red}{(16q^2)}^2=16-256q^{4}\)
11. \((-15s^2-4)(-15s^2-4)=(-15s^2-4)^2=(-15s^2)^2\color{magenta}{+2.(-15s^2).(-4)}+(-4)^2=225s^{4}\color{magenta}{+120s^2}+16\)
12. \((q-3)(q-3)=(q-3)^2=q^2+\color{magenta}{2.q.(-3)}+(-3)^2=q^2\color{magenta}{-6q}+9\)