Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{blue}{q}\color{red}{-4})(\color{blue}{q}\color{red}{+4})=\color{blue}{q}^2-\color{red}{4}^2=q^2-16\)
2. \((-13p^5-5)^2=(-13p^5)^2\color{magenta}{+2.(-13p^5).(-5)}+(-5)^2=169p^{10}\color{magenta}{+130p^5}+25\)
3. \((\color{blue}{-16q^5}\color{red}{-15p})(\color{blue}{-16q^5}\color{red}{+15p})=\color{blue}{(-16q^5)}^2-\color{red}{(-15p)}^2=256q^{10}-225p^2\)
4. \((5b^2+11)^2=(5b^2)^2\color{magenta}{+2.(5b^2).11}+11^2=25b^{4}\color{magenta}{+110b^2}+121\)
5. \((\color{red}{9s^2}\color{blue}{-2})(\color{red}{-9s^2}\color{blue}{-2})=\color{blue}{(-2)}^2-\color{red}{(9s^2)}^2=4-81s^{4}\)
6. \((\color{blue}{4a}\color{red}{+7})(\color{blue}{4a}\color{red}{-7})=\color{blue}{(4a)}^2-\color{red}{(7)}^2=16a^2-49\)
7. \((-2a-3)^2=(-2a)^2+\color{magenta}{2.(-2a).(-3)}+(-3)^2=4a^2\color{magenta}{+12a}+9\)
8. \((\color{red}{-5x}\color{blue}{+2})(\color{red}{5x}\color{blue}{+2})=\color{blue}{2}^2-\color{red}{(5x)}^2=4-25x^2\)
9. \((13p^5-14x)^2=(13p^5)^2\color{magenta}{+2.(13p^5).(-14x)}+(-14x)^2=169p^{10}\color{magenta}{-364p^5x}+196x^2\)
10. \((\color{red}{-4b^2}\color{blue}{+2})(\color{red}{4b^2}\color{blue}{+2})=\color{blue}{2}^2-\color{red}{(4b^2)}^2=4-16b^{4}\)
11. \((\color{red}{5q^4}\color{blue}{+5p})(\color{red}{-5q^4}\color{blue}{+5p})=\color{blue}{(5p)}^2-\color{red}{(5q^4)}^2=25p^2-25q^{8}\)
12. \((\color{blue}{9p^4}\color{red}{+7})(\color{blue}{9p^4}\color{red}{-7})=\color{blue}{(9p^4)}^2-\color{red}{7}^2=81p^{8}-49\)