Merkwaardige producten (MP)

Hoofdmenu Eentje per keer  🖨

Bereken de volgende merkwaardige producten

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

---

Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((15b+4)^2=(15b)^2+\color{magenta}{2.(15b).4}+4^2=225b^2\color{magenta}{+120b}+16\)
2. \((\color{blue}{p}\color{red}{+5})(\color{blue}{p}\color{red}{-5})=\color{blue}{p}^2-\color{red}{5}^2=p^2-25\)
3. \((\color{red}{-4s^4}\color{blue}{+4})(\color{red}{4s^4}\color{blue}{+4})=\color{blue}{4}^2-\color{red}{(4s^4)}^2=16-16s^{8}\)
4. \((\color{red}{-5s^5}\color{blue}{-6})(\color{red}{5s^5}\color{blue}{-6})=\color{blue}{(-6)}^2-\color{red}{(5s^5)}^2=36-25s^{10}\)
5. \((q+7)(q+7)=(q+7)^2=q^2+\color{magenta}{2.q.7}+7^2=q^2\color{magenta}{+14q}+49\)
6. \((q-7)^2=q^2+\color{magenta}{2.q.(-7)}+(-7)^2=q^2\color{magenta}{-14q}+49\)
7. \((\color{blue}{a}\color{red}{-8})(\color{blue}{a}\color{red}{+8})=\color{blue}{a}^2-\color{red}{8}^2=a^2-64\)
8. \((9y-13)(9y-13)=(9y-13)^2=(9y)^2+\color{magenta}{2.(9y).(-13)}+(-13)^2=81y^2\color{magenta}{-234y}+169\)
9. \((\color{blue}{-14s}\color{red}{-7})(\color{blue}{-14s}\color{red}{+7})=\color{blue}{(-14s)}^2-\color{red}{(-7)}^2=196s^2-49\)
10. \((\color{blue}{-5a^3}\color{red}{+5})(\color{blue}{-5a^3}\color{red}{-5})=\color{blue}{(-5a^3)}^2-\color{red}{5}^2=25a^{6}-25\)
11. \((\color{red}{3s}\color{blue}{+10})(\color{red}{-3s}\color{blue}{+10})=\color{blue}{10}^2-\color{red}{(3s)}^2=100-9s^2\)
12. \((\color{blue}{p}\color{red}{-2})(\color{blue}{p}\color{red}{+2})=\color{blue}{p}^2-\color{red}{2}^2=p^2-4\)