Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{blue}{-5b^5}\color{red}{+5y})(\color{blue}{-5b^5}\color{red}{-5y})=\color{blue}{(-5b^5)}^2-\color{red}{(5y)}^2=25b^{10}-25y^2\)
2. \((\color{blue}{a}\color{red}{-11})(\color{blue}{a}\color{red}{+11})=\color{blue}{a}^2-\color{red}{11}^2=a^2-121\)
3. \((-5a-6)^2=(-5a)^2+\color{magenta}{2.(-5a).(-6)}+(-6)^2=25a^2\color{magenta}{+60a}+36\)
4. \((-y^4-8p)(-y^4-8p)=(-y^4-8p)^2=(-y^4)^2\color{magenta}{+2.(-y^4).(-8p)}+(-8p)^2=y^{8}\color{magenta}{+16py^4}+64p^2\)
5. \((\color{red}{-10y}\color{blue}{-14})(\color{red}{10y}\color{blue}{-14})=\color{blue}{(-14)}^2-\color{red}{(10y)}^2=196-100y^2\)
6. \((10p^5-8)(10p^5-8)=(10p^5-8)^2=(10p^5)^2\color{magenta}{+2.(10p^5).(-8)}+(-8)^2=100p^{10}\color{magenta}{-160p^5}+64\)
7. \((s-15)(s-15)=(s-15)^2=s^2+\color{magenta}{2.s.(-15)}+(-15)^2=s^2\color{magenta}{-30s}+225\)
8. \((\color{red}{-5b^2}\color{blue}{+16})(\color{red}{5b^2}\color{blue}{+16})=\color{blue}{16}^2-\color{red}{(5b^2)}^2=256-25b^{4}\)
9. \((\color{blue}{-2p^2}\color{red}{-1})(\color{blue}{-2p^2}\color{red}{+1})=\color{blue}{(-2p^2)}^2-\color{red}{(-1)}^2=4p^{4}-1\)
10. \((-13b^4-15p)(-13b^4-15p)=(-13b^4-15p)^2=(-13b^4)^2\color{magenta}{+2.(-13b^4).(-15p)}+(-15p)^2=169b^{8}\color{magenta}{+390b^4p}+225p^2\)
11. \((q-2)^2=q^2+\color{magenta}{2.q.(-2)}+(-2)^2=q^2\color{magenta}{-4q}+4\)
12. \((12x^4-1)^2=(12x^4)^2\color{magenta}{+2.(12x^4).(-1)}+(-1)^2=144x^{8}\color{magenta}{-24x^4}+1\)