Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((-16y^4-2)^2=(-16y^4)^2\color{magenta}{+2.(-16y^4).(-2)}+(-2)^2=256y^{8}\color{magenta}{+64y^4}+4\)
2. \((-4q-4)(-4q-4)=(-4q-4)^2=(-4q)^2+\color{magenta}{2.(-4q).(-4)}+(-4)^2=16q^2\color{magenta}{+32q}+16\)
3. \((\color{red}{12y}\color{blue}{-4})(\color{red}{-12y}\color{blue}{-4})=\color{blue}{(-4)}^2-\color{red}{(12y)}^2=16-144y^2\)
4. \((15y^5+16)^2=(15y^5)^2\color{magenta}{+2.(15y^5).16}+16^2=225y^{10}\color{magenta}{+480y^5}+256\)
5. \((\color{blue}{s}\color{red}{+6})(\color{blue}{s}\color{red}{-6})=\color{blue}{s}^2-\color{red}{6}^2=s^2-36\)
6. \((\color{blue}{-2p}\color{red}{-14})(\color{blue}{-2p}\color{red}{+14})=\color{blue}{(-2p)}^2-\color{red}{(-14)}^2=4p^2-196\)
7. \((\color{red}{8p^3}\color{blue}{+7})(\color{red}{-8p^3}\color{blue}{+7})=\color{blue}{7}^2-\color{red}{(8p^3)}^2=49-64p^{6}\)
8. \((-10b+12)^2=(-10b)^2+\color{magenta}{2.(-10b).12}+12^2=100b^2\color{magenta}{-240b}+144\)
9. \((\color{blue}{s}\color{red}{-6})(\color{blue}{s}\color{red}{+6})=\color{blue}{s}^2-\color{red}{6}^2=s^2-36\)
10. \((\color{blue}{-16a^5}\color{red}{-8y})(\color{blue}{-16a^5}\color{red}{+8y})=\color{blue}{(-16a^5)}^2-\color{red}{(-8y)}^2=256a^{10}-64y^2\)
11. \((q-1)^2=q^2+\color{magenta}{2.q.(-1)}+(-1)^2=q^2\color{magenta}{-2q}+1\)
12. \((-15x^4+6)^2=(-15x^4)^2\color{magenta}{+2.(-15x^4).6}+6^2=225x^{8}\color{magenta}{-180x^4}+36\)