Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{blue}{b}\color{red}{+2})(\color{blue}{b}\color{red}{-2})=\color{blue}{b}^2-\color{red}{2}^2=b^2-4\)
2. \((\color{red}{15s}\color{blue}{+11})(\color{red}{-15s}\color{blue}{+11})=\color{blue}{11}^2-\color{red}{(15s)}^2=121-225s^2\)
3. \((\color{blue}{5q^3}\color{red}{-10a})(\color{blue}{5q^3}\color{red}{+10a})=\color{blue}{(5q^3)}^2-\color{red}{(-10a)}^2=25q^{6}-100a^2\)
4. \((-12a^4-6b)(-12a^4-6b)=(-12a^4-6b)^2=(-12a^4)^2\color{magenta}{+2.(-12a^4).(-6b)}+(-6b)^2=144a^{8}\color{magenta}{+144a^4b}+36b^2\)
5. \((\color{blue}{-16x}\color{red}{-10})(\color{blue}{-16x}\color{red}{+10})=\color{blue}{(-16x)}^2-\color{red}{(-10)}^2=256x^2-100\)
6. \((b+8)(b+8)=(b+8)^2=b^2+\color{magenta}{2.b.8}+8^2=b^2\color{magenta}{+16b}+64\)
7. \((\color{red}{-9b^4}\color{blue}{+16y})(\color{red}{9b^4}\color{blue}{+16y})=\color{blue}{(16y)}^2-\color{red}{(9b^4)}^2=256y^2-81b^{8}\)
8. \((-11y^5+10)^2=(-11y^5)^2\color{magenta}{+2.(-11y^5).10}+10^2=121y^{10}\color{magenta}{-220y^5}+100\)
9. \((\color{red}{12a^5}\color{blue}{-1})(\color{red}{-12a^5}\color{blue}{-1})=\color{blue}{(-1)}^2-\color{red}{(12a^5)}^2=1-144a^{10}\)
10. \((\color{red}{-9y^5}\color{blue}{-16p})(\color{red}{9y^5}\color{blue}{-16p})=\color{blue}{(-16p)}^2-\color{red}{(9y^5)}^2=256p^2-81y^{10}\)
11. \((-13p^5+15b)^2=(-13p^5)^2\color{magenta}{+2.(-13p^5).(15b)}+(15b)^2=169p^{10}\color{magenta}{-390bp^5}+225b^2\)
12. \((2q^5-13)^2=(2q^5)^2\color{magenta}{+2.(2q^5).(-13)}+(-13)^2=4q^{10}\color{magenta}{-52q^5}+169\)