Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{red}{-16x^4}\color{blue}{+5p})(\color{red}{16x^4}\color{blue}{+5p})=\color{blue}{(5p)}^2-\color{red}{(16x^4)}^2=25p^2-256x^{8}\)
2. \((-3y^5-3a)(-3y^5-3a)=(-3y^5-3a)^2=(-3y^5)^2\color{magenta}{+2.(-3y^5).(-3a)}+(-3a)^2=9y^{10}\color{magenta}{+18ay^5}+9a^2\)
3. \((\color{blue}{y}\color{red}{-11})(\color{blue}{y}\color{red}{+11})=\color{blue}{y}^2-\color{red}{11}^2=y^2-121\)
4. \((\color{blue}{13q^2}\color{red}{-13})(\color{blue}{13q^2}\color{red}{+13})=\color{blue}{(13q^2)}^2-\color{red}{(-13)}^2=169q^{4}-169\)
5. \((\color{blue}{s}\color{red}{-12})(\color{blue}{s}\color{red}{+12})=\color{blue}{s}^2-\color{red}{12}^2=s^2-144\)
6. \((-9y+7)(-9y+7)=(-9y+7)^2=(-9y)^2+\color{magenta}{2.(-9y).7}+7^2=81y^2\color{magenta}{-126y}+49\)
7. \((4y^2+4a)(4y^2+4a)=(4y^2+4a)^2=(4y^2)^2\color{magenta}{+2.(4y^2).(4a)}+(4a)^2=16y^{4}\color{magenta}{+32ay^2}+16a^2\)
8. \((p-10)(p-10)=(p-10)^2=(p)^2+\color{magenta}{2.(p).(-10)}+(-10)^2=p^2\color{magenta}{-20p}+100\)
9. \((\color{red}{13s^4}\color{blue}{+13})(\color{red}{-13s^4}\color{blue}{+13})=\color{blue}{13}^2-\color{red}{(13s^4)}^2=169-169s^{8}\)
10. \((a-13)(a-13)=(a-13)^2=a^2+\color{magenta}{2.a.(-13)}+(-13)^2=a^2\color{magenta}{-26a}+169\)
11. \((16q-14)(16q-14)=(16q-14)^2=(16q)^2+\color{magenta}{2.(16q).(-14)}+(-14)^2=256q^2\color{magenta}{-448q}+196\)
12. \((\color{red}{16q}\color{blue}{-11})(\color{red}{-16q}\color{blue}{-11})=\color{blue}{(-11)}^2-\color{red}{(16q)}^2=121-256q^2\)