Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{red}{3p}\color{blue}{+11})(\color{red}{-3p}\color{blue}{+11})=\color{blue}{11}^2-\color{red}{(3p)}^2=121-9p^2\)
2. \((8x^5-13)(8x^5-13)=(8x^5-13)^2=(8x^5)^2\color{magenta}{+2.(8x^5).(-13)}+(-13)^2=64x^{10}\color{magenta}{-208x^5}+169\)
3. \((\color{blue}{b}\color{red}{+8})(\color{blue}{b}\color{red}{-8})=\color{blue}{b}^2-\color{red}{8}^2=b^2-64\)
4. \((\color{blue}{-12b^2}\color{red}{-2})(\color{blue}{-12b^2}\color{red}{+2})=\color{blue}{(-12b^2)}^2-\color{red}{(-2)}^2=144b^{4}-4\)
5. \((b+5)^2=b^2+\color{magenta}{2.b.5}+5^2=b^2\color{magenta}{+10b}+25\)
6. \((\color{red}{14y^5}\color{blue}{+10})(\color{red}{-14y^5}\color{blue}{+10})=\color{blue}{10}^2-\color{red}{(14y^5)}^2=100-196y^{10}\)
7. \((9p-2)^2=(9p)^2+\color{magenta}{2.(9p).(-2)}+(-2)^2=81p^2\color{magenta}{-36p}+4\)
8. \((15q+6)(15q+6)=(15q+6)^2=(15q)^2+\color{magenta}{2.(15q).6}+6^2=225q^2\color{magenta}{+180q}+36\)
9. \((-15x^3-12)^2=(-15x^3)^2\color{magenta}{+2.(-15x^3).(-12)}+(-12)^2=225x^{6}\color{magenta}{+360x^3}+144\)
10. \((\color{red}{-12q^2}\color{blue}{+a})(\color{red}{12q^2}\color{blue}{+a})=\color{blue}{(1a)}^2-\color{red}{(12q^2)}^2=1a^2-144q^{4}\)
11. \((q-2)^2=q^2+\color{magenta}{2.q.(-2)}+(-2)^2=q^2\color{magenta}{-4q}+4\)
12. \((\color{blue}{-8x}\color{red}{+13})(\color{blue}{-8x}\color{red}{-13})=\color{blue}{(-8x)}^2-\color{red}{(13)}^2=64x^2-169\)