Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((-6p+16)(-6p+16)=(-6p+16)^2=(-6p)^2+\color{magenta}{2.(-6p).16}+16^2=36p^2\color{magenta}{-192p}+256\)
2. \((x-9)^2=x^2+\color{magenta}{2.x.(-9)}+(-9)^2=x^2\color{magenta}{-18x}+81\)
3. \((\color{red}{11s^4}\color{blue}{-9x})(\color{red}{-11s^4}\color{blue}{-9x})=\color{blue}{(-9x)}^2-\color{red}{(11s^4)}^2=81x^2-121s^{8}\)
4. \((\color{blue}{q}\color{red}{+13})(\color{blue}{q}\color{red}{-13})=\color{blue}{q}^2-\color{red}{13}^2=q^2-169\)
5. \((\color{blue}{-b}\color{red}{+16})(\color{blue}{-b}\color{red}{-16})=\color{blue}{(-b)}^2-\color{red}{(16)}^2=b^2-256\)
6. \((\color{blue}{-q^4}\color{red}{-5})(\color{blue}{-q^4}\color{red}{+5})=\color{blue}{(-q^4)}^2-\color{red}{(-5)}^2=q^{8}-25\)
7. \((\color{red}{16x}\color{blue}{+4})(\color{red}{-16x}\color{blue}{+4})=\color{blue}{4}^2-\color{red}{(16x)}^2=16-256x^2\)
8. \((-8s^3+4)^2=(-8s^3)^2\color{magenta}{+2.(-8s^3).4}+4^2=64s^{6}\color{magenta}{-64s^3}+16\)
9. \((\color{blue}{8a^4}\color{red}{-5q})(\color{blue}{8a^4}\color{red}{+5q})=\color{blue}{(8a^4)}^2-\color{red}{(-5q)}^2=64a^{8}-25q^2\)
10. \((15s^5+6)(15s^5+6)=(15s^5+6)^2=(15s^5)^2\color{magenta}{+2.(15s^5).6}+6^2=225s^{10}\color{magenta}{+180s^5}+36\)
11. \((s+14)(s+14)=(s+14)^2=s^2+\color{magenta}{2.s.14}+14^2=s^2\color{magenta}{+28s}+196\)
12. \((s^3+8)^2=(s^3)^2\color{magenta}{+2.(s^3).8}+8^2=1s^{6}\color{magenta}{+16s^3}+64\)