Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((a+11)^2=a^2+\color{magenta}{2.a.11}+11^2=a^2\color{magenta}{+22a}+121\)
2. \((7p+5)(7p+5)=(7p+5)^2=(7p)^2+\color{magenta}{2.(7p).5}+5^2=49p^2\color{magenta}{+70p}+25\)
3. \((\color{blue}{p}\color{red}{-1})(\color{blue}{p}\color{red}{+1})=\color{blue}{p}^2-\color{red}{1}^2=p^2-1\)
4. \((\color{blue}{b}\color{red}{-15})(\color{blue}{b}\color{red}{+15})=\color{blue}{b}^2-\color{red}{15}^2=b^2-225\)
5. \((8b^3-12p)(8b^3-12p)=(8b^3-12p)^2=(8b^3)^2\color{magenta}{+2.(8b^3).(-12p)}+(-12p)^2=64b^{6}\color{magenta}{-192b^3p}+144p^2\)
6. \((x+7)^2=x^2+\color{magenta}{2.x.7}+7^2=x^2\color{magenta}{+14x}+49\)
7. \((\color{red}{-3q^5}\color{blue}{-8})(\color{red}{3q^5}\color{blue}{-8})=\color{blue}{(-8)}^2-\color{red}{(3q^5)}^2=64-9q^{10}\)
8. \((\color{red}{15b^2}\color{blue}{-13})(\color{red}{-15b^2}\color{blue}{-13})=\color{blue}{(-13)}^2-\color{red}{(15b^2)}^2=169-225b^{4}\)
9. \((-6x^3-10)(-6x^3-10)=(-6x^3-10)^2=(-6x^3)^2\color{magenta}{+2.(-6x^3).(-10)}+(-10)^2=36x^{6}\color{magenta}{+120x^3}+100\)
10. \((\color{blue}{-11x^2}\color{red}{+4})(\color{blue}{-11x^2}\color{red}{-4})=\color{blue}{(-11x^2)}^2-\color{red}{4}^2=121x^{4}-16\)
11. \((\color{blue}{-11s^3}\color{red}{+x})(\color{blue}{-11s^3}\color{red}{-x})=\color{blue}{(-11s^3)}^2-\color{red}{(1x)}^2=121s^{6}-1x^2\)
12. \((11y-2)^2=(11y)^2+\color{magenta}{2.(11y).(-2)}+(-2)^2=121y^2\color{magenta}{-44y}+4\)