Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((13p^2+11x)^2=(13p^2)^2\color{magenta}{+2.(13p^2).(11x)}+(11x)^2=169p^{4}\color{magenta}{+286p^2x}+121x^2\)
2. \((-13a-13)(-13a-13)=(-13a-13)^2=(-13a)^2+\color{magenta}{2.(-13a).(-13)}+(-13)^2=169a^2\color{magenta}{+338a}+169\)
3. \((q+5)(q+5)=(q+5)^2=q^2+\color{magenta}{2.q.5}+5^2=q^2\color{magenta}{+10q}+25\)
4. \((\color{blue}{12a^5}\color{red}{+8q})(\color{blue}{12a^5}\color{red}{-8q})=\color{blue}{(12a^5)}^2-\color{red}{(8q)}^2=144a^{10}-64q^2\)
5. \((\color{blue}{-9b^5}\color{red}{-15})(\color{blue}{-9b^5}\color{red}{+15})=\color{blue}{(-9b^5)}^2-\color{red}{(-15)}^2=81b^{10}-225\)
6. \((\color{blue}{16p}\color{red}{+7})(\color{blue}{16p}\color{red}{-7})=\color{blue}{(16p)}^2-\color{red}{(7)}^2=256p^2-49\)
7. \((-15q+8)^2=(-15q)^2+\color{magenta}{2.(-15q).8}+8^2=225q^2\color{magenta}{-240q}+64\)
8. \((13a^2+3)^2=(13a^2)^2\color{magenta}{+2.(13a^2).3}+3^2=169a^{4}\color{magenta}{+78a^2}+9\)
9. \((\color{red}{-13s}\color{blue}{-10})(\color{red}{13s}\color{blue}{-10})=\color{blue}{(-10)}^2-\color{red}{(13s)}^2=100-169s^2\)
10. \((\color{blue}{b}\color{red}{-5})(\color{blue}{b}\color{red}{+5})=\color{blue}{b}^2-\color{red}{5}^2=b^2-25\)
11. \((\color{blue}{-5a^5}\color{red}{+12})(\color{blue}{-5a^5}\color{red}{-12})=\color{blue}{(-5a^5)}^2-\color{red}{12}^2=25a^{10}-144\)
12. \((\color{blue}{x}\color{red}{-13})(\color{blue}{x}\color{red}{+13})=\color{blue}{x}^2-\color{red}{13}^2=x^2-169\)