Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{blue}{-4a}\color{red}{+13})(\color{blue}{-4a}\color{red}{-13})=\color{blue}{(-4a)}^2-\color{red}{(13)}^2=16a^2-169\)
2. \((\color{red}{6p^5}\color{blue}{+5})(\color{red}{-6p^5}\color{blue}{+5})=\color{blue}{5}^2-\color{red}{(6p^5)}^2=25-36p^{10}\)
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. \((\color{blue}{y}\color{red}{+6})(\color{blue}{y}\color{red}{-6})=\color{blue}{y}^2-\color{red}{6}^2=y^2-36\)
5. \((\color{blue}{a}\color{red}{+8})(\color{blue}{a}\color{red}{-8})=\color{blue}{(a)}^2-\color{red}{(8)}^2=a^2-64\)
6. \((11q+11)^2=(11q)^2+\color{magenta}{2.(11q).11}+11^2=121q^2\color{magenta}{+242q}+121\)
7. \((15p^5-7a)^2=(15p^5)^2\color{magenta}{+2.(15p^5).(-7a)}+(-7a)^2=225p^{10}\color{magenta}{-210ap^5}+49a^2\)
8. \((-10q^5-2y)^2=(-10q^5)^2\color{magenta}{+2.(-10q^5).(-2y)}+(-2y)^2=100q^{10}\color{magenta}{+40q^5y}+4y^2\)
9. \((\color{red}{-x^3}\color{blue}{+6b})(\color{red}{x^3}\color{blue}{+6b})=\color{blue}{(6b)}^2-\color{red}{(x^3)}^2=36b^2-x^{6}\)
10. \((\color{blue}{-2x^2}\color{red}{-12a})(\color{blue}{-2x^2}\color{red}{+12a})=\color{blue}{(-2x^2)}^2-\color{red}{(-12a)}^2=4x^{4}-144a^2\)
11. \((-6q^3+16a)(-6q^3+16a)=(-6q^3+16a)^2=(-6q^3)^2\color{magenta}{+2.(-6q^3).(16a)}+(16a)^2=36q^{6}\color{magenta}{-192aq^3}+256a^2\)
12. \((\color{blue}{s}\color{red}{+12})(\color{blue}{s}\color{red}{-12})=\color{blue}{s}^2-\color{red}{12}^2=s^2-144\)