Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{blue}{x}\color{red}{+1})(\color{blue}{x}\color{red}{-1})=\color{blue}{x}^2-\color{red}{1}^2=x^2-1\)
2. \((\color{red}{2a}\color{blue}{-8})(\color{red}{-2a}\color{blue}{-8})=\color{blue}{(-8)}^2-\color{red}{(2a)}^2=64-4a^2\)
3. \((\color{blue}{-5a}\color{red}{+7})(\color{blue}{-5a}\color{red}{-7})=\color{blue}{(-5a)}^2-\color{red}{(7)}^2=25a^2-49\)
4. \((\color{blue}{a}\color{red}{+8})(\color{blue}{a}\color{red}{-8})=\color{blue}{a}^2-\color{red}{8}^2=a^2-64\)
5. \((\color{red}{10b^3}\color{blue}{-16})(\color{red}{-10b^3}\color{blue}{-16})=\color{blue}{(-16)}^2-\color{red}{(10b^3)}^2=256-100b^{6}\)
6. \((\color{red}{-11b^3}\color{blue}{+1})(\color{red}{11b^3}\color{blue}{+1})=\color{blue}{1}^2-\color{red}{(11b^3)}^2=1-121b^{6}\)
7. \((\color{red}{12a^3}\color{blue}{+16x})(\color{red}{-12a^3}\color{blue}{+16x})=\color{blue}{(16x)}^2-\color{red}{(12a^3)}^2=256x^2-144a^{6}\)
8. \((\color{red}{-16p^4}\color{blue}{+16q})(\color{red}{16p^4}\color{blue}{+16q})=\color{blue}{(16q)}^2-\color{red}{(16p^4)}^2=256q^2-256p^{8}\)
9. \((-16b^4+4x)^2=(-16b^4)^2\color{magenta}{+2.(-16b^4).(4x)}+(4x)^2=256b^{8}\color{magenta}{-128b^4x}+16x^2\)
10. \((-p^5-5)(-p^5-5)=(-p^5-5)^2=(-p^5)^2\color{magenta}{+2.(-p^5).(-5)}+(-5)^2=1p^{10}\color{magenta}{+10p^5}+25\)
11. \((\color{red}{-15q}\color{blue}{-10})(\color{red}{15q}\color{blue}{-10})=\color{blue}{(-10)}^2-\color{red}{(15q)}^2=100-225q^2\)
12. \((\color{red}{16p^3}\color{blue}{-6})(\color{red}{-16p^3}\color{blue}{-6})=\color{blue}{(-6)}^2-\color{red}{(16p^3)}^2=36-256p^{6}\)