Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{red}{14b^3}\color{blue}{-13})(\color{red}{-14b^3}\color{blue}{-13})=\color{blue}{(-13)}^2-\color{red}{(14b^3)}^2=169-196b^{6}\)
2. \((a+8)(a+8)=(a+8)^2=a^2+\color{magenta}{2.a.8}+8^2=a^2\color{magenta}{+16a}+64\)
3. \((\color{blue}{8y^5}\color{red}{-4p})(\color{blue}{8y^5}\color{red}{+4p})=\color{blue}{(8y^5)}^2-\color{red}{(-4p)}^2=64y^{10}-16p^2\)
4. \((11a+16)^2=(11a)^2+\color{magenta}{2.(11a).16}+16^2=121a^2\color{magenta}{+352a}+256\)
5. \((b-15)^2=b^2+\color{magenta}{2.b.(-15)}+(-15)^2=b^2\color{magenta}{-30b}+225\)
6. \((\color{red}{-15q}\color{blue}{-1})(\color{red}{15q}\color{blue}{-1})=\color{blue}{(-1)}^2-\color{red}{(15q)}^2=1-225q^2\)
7. \((a-12)(a-12)=(a-12)^2=a^2+\color{magenta}{2.a.(-12)}+(-12)^2=a^2\color{magenta}{-24a}+144\)
8. \((\color{blue}{2q}\color{red}{-11})(\color{blue}{2q}\color{red}{+11})=\color{blue}{(2q)}^2-\color{red}{(-11)}^2=4q^2-121\)
9. \((\color{blue}{-3a}\color{red}{-2})(\color{blue}{-3a}\color{red}{+2})=\color{blue}{(-3a)}^2-\color{red}{(-2)}^2=9a^2-4\)
10. \((-10a^5-4)^2=(-10a^5)^2\color{magenta}{+2.(-10a^5).(-4)}+(-4)^2=100a^{10}\color{magenta}{+80a^5}+16\)
11. \((\color{red}{8p}\color{blue}{-4})(\color{red}{-8p}\color{blue}{-4})=\color{blue}{(-4)}^2-\color{red}{(8p)}^2=16-64p^2\)
12. \((\color{blue}{p}\color{red}{+10})(\color{blue}{p}\color{red}{-10})=\color{blue}{p}^2-\color{red}{10}^2=p^2-100\)