Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((-14a^4+2s)(-14a^4+2s)=(-14a^4+2s)^2=(-14a^4)^2\color{magenta}{+2.(-14a^4).(2s)}+(2s)^2=196a^{8}\color{magenta}{-56a^4s}+4s^2\)
2. \((16q+4)(16q+4)=(16q+4)^2=(16q)^2+\color{magenta}{2.(16q).4}+4^2=256q^2\color{magenta}{+128q}+16\)
3. \((p-10)(p-10)=(p-10)^2=p^2+\color{magenta}{2.p.(-10)}+(-10)^2=p^2\color{magenta}{-20p}+100\)
4. \((-5b^4+6s)^2=(-5b^4)^2\color{magenta}{+2.(-5b^4).(6s)}+(6s)^2=25b^{8}\color{magenta}{-60b^4s}+36s^2\)
5. \((\color{red}{4b^3}\color{blue}{+13})(\color{red}{-4b^3}\color{blue}{+13})=\color{blue}{13}^2-\color{red}{(4b^3)}^2=169-16b^{6}\)
6. \((y-2)^2=y^2+\color{magenta}{2.y.(-2)}+(-2)^2=y^2\color{magenta}{-4y}+4\)
7. \((-16s+12)(-16s+12)=(-16s+12)^2=(-16s)^2+\color{magenta}{2.(-16s).12}+12^2=256s^2\color{magenta}{-384s}+144\)
8. \((10b^3-15)^2=(10b^3)^2\color{magenta}{+2.(10b^3).(-15)}+(-15)^2=100b^{6}\color{magenta}{-300b^3}+225\)
9. \((2s^5+4)^2=(2s^5)^2\color{magenta}{+2.(2s^5).4}+4^2=4s^{10}\color{magenta}{+16s^5}+16\)
10. \((\color{blue}{a^3}\color{red}{-4s})(\color{blue}{a^3}\color{red}{+4s})=\color{blue}{(a^3)}^2-\color{red}{(-4s)}^2=a^{6}-16s^2\)
11. \((-6b-15)^2=(-6b)^2+\color{magenta}{2.(-6b).(-15)}+(-15)^2=36b^2\color{magenta}{+180b}+225\)
12. \((\color{red}{-9a^3}\color{blue}{+8p})(\color{red}{9a^3}\color{blue}{+8p})=\color{blue}{(8p)}^2-\color{red}{(9a^3)}^2=64p^2-81a^{6}\)