Merkwaardige producten (MP)

Hoofdmenu Eentje per keer  🖨

Bereken de volgende merkwaardige producten

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

---

Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{red}{-10y^5}\color{blue}{+14})(\color{red}{10y^5}\color{blue}{+14})=\color{blue}{14}^2-\color{red}{(10y^5)}^2=196-100y^{10}\)
2. \((\color{blue}{15a^3}\color{red}{+1})(\color{blue}{15a^3}\color{red}{-1})=\color{blue}{(15a^3)}^2-\color{red}{1}^2=225a^{6}-1\)
3. \((\color{blue}{16s}\color{red}{-7})(\color{blue}{16s}\color{red}{+7})=\color{blue}{(16s)}^2-\color{red}{(-7)}^2=256s^2-49\)
4. \((\color{red}{10y}\color{blue}{+14})(\color{red}{-10y}\color{blue}{+14})=\color{blue}{14}^2-\color{red}{(10y)}^2=196-100y^2\)
5. \((a-9)^2=a^2+\color{magenta}{2.a.(-9)}+(-9)^2=a^2\color{magenta}{-18a}+81\)
6. \((\color{blue}{14q^2}\color{red}{-14})(\color{blue}{14q^2}\color{red}{+14})=\color{blue}{(14q^2)}^2-\color{red}{(-14)}^2=196q^{4}-196\)
7. \((4s^4-3)^2=(4s^4)^2\color{magenta}{+2.(4s^4).(-3)}+(-3)^2=16s^{8}\color{magenta}{-24s^4}+9\)
8. \((a+8)^2=a^2+\color{magenta}{2.a.8}+8^2=a^2\color{magenta}{+16a}+64\)
9. \((11b-1)(11b-1)=(11b-1)^2=(11b)^2+\color{magenta}{2.(11b).(-1)}+(-1)^2=121b^2\color{magenta}{-22b}+1\)
10. \((\color{blue}{p}\color{red}{-9})(\color{blue}{p}\color{red}{+9})=\color{blue}{p}^2-\color{red}{9}^2=p^2-81\)
11. \((\color{blue}{q}\color{red}{-14})(\color{blue}{q}\color{red}{+14})=\color{blue}{q}^2-\color{red}{14}^2=q^2-196\)
12. \((\color{red}{13y^2}\color{blue}{-8s})(\color{red}{-13y^2}\color{blue}{-8s})=\color{blue}{(-8s)}^2-\color{red}{(13y^2)}^2=64s^2-169y^{4}\)