Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((-15x+16)(-15x+16)=(-15x+16)^2=(-15x)^2+\color{magenta}{2.(-15x).16}+16^2=225x^2\color{magenta}{-480x}+256\)
2. \((\color{red}{4y^2}\color{blue}{-2})(\color{red}{-4y^2}\color{blue}{-2})=\color{blue}{(-2)}^2-\color{red}{(4y^2)}^2=4-16y^{4}\)
3. \((\color{red}{16y^4}\color{blue}{-4q})(\color{red}{-16y^4}\color{blue}{-4q})=\color{blue}{(-4q)}^2-\color{red}{(16y^4)}^2=16q^2-256y^{8}\)
4. \((-q+15)(-q+15)=(-q+15)^2=(-q)^2+\color{magenta}{2.(-q).15}+15^2=q^2\color{magenta}{-30q}+225\)
5. \((x-3)(x-3)=(x-3)^2=x^2+\color{magenta}{2.x.(-3)}+(-3)^2=x^2\color{magenta}{-6x}+9\)
6. \((\color{blue}{p}\color{red}{+7})(\color{blue}{p}\color{red}{-7})=\color{blue}{p}^2-\color{red}{7}^2=p^2-49\)
7. \((10a-2)^2=(10a)^2+\color{magenta}{2.(10a).(-2)}+(-2)^2=100a^2\color{magenta}{-40a}+4\)
8. \((-13p^5+4a)(-13p^5+4a)=(-13p^5+4a)^2=(-13p^5)^2\color{magenta}{+2.(-13p^5).(4a)}+(4a)^2=169p^{10}\color{magenta}{-104ap^5}+16a^2\)
9. \((\color{red}{13a^5}\color{blue}{+13p})(\color{red}{-13a^5}\color{blue}{+13p})=\color{blue}{(13p)}^2-\color{red}{(13a^5)}^2=169p^2-169a^{10}\)
10. \((\color{blue}{y}\color{red}{-6})(\color{blue}{y}\color{red}{+6})=\color{blue}{y}^2-\color{red}{6}^2=y^2-36\)
11. \((q+2)(q+2)=(q+2)^2=q^2+\color{magenta}{2.q.2}+2^2=q^2\color{magenta}{+4q}+4\)
12. \((a+4)^2=a^2+\color{magenta}{2.a.4}+4^2=a^2\color{magenta}{+8a}+16\)