Merkwaardige producten (MP)

Hoofdmenu Eentje per keer  🖨

Bereken de volgende merkwaardige producten

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

---

Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((a+3)(a+3)=(a+3)^2=a^2+\color{magenta}{2.a.3}+3^2=a^2\color{magenta}{+6a}+9\)
2. \((q+7)(q+7)=(q+7)^2=q^2+\color{magenta}{2.q.7}+7^2=q^2\color{magenta}{+14q}+49\)
3. \((10s^4+3y)^2=(10s^4)^2\color{magenta}{+2.(10s^4).(3y)}+(3y)^2=100s^{8}\color{magenta}{+60s^4y}+9y^2\)
4. \((\color{red}{-y^5}\color{blue}{+7a})(\color{red}{y^5}\color{blue}{+7a})=\color{blue}{(7a)}^2-\color{red}{(y^5)}^2=49a^2-y^{10}\)
5. \((9a^3+10)^2=(9a^3)^2\color{magenta}{+2.(9a^3).10}+10^2=81a^{6}\color{magenta}{+180a^3}+100\)
6. \((\color{red}{-3p^4}\color{blue}{+4})(\color{red}{3p^4}\color{blue}{+4})=\color{blue}{4}^2-\color{red}{(3p^4)}^2=16-9p^{8}\)
7. \((14b^2-16)^2=(14b^2)^2\color{magenta}{+2.(14b^2).(-16)}+(-16)^2=196b^{4}\color{magenta}{-448b^2}+256\)
8. \((10y-3)(10y-3)=(10y-3)^2=(10y)^2+\color{magenta}{2.(10y).(-3)}+(-3)^2=100y^2\color{magenta}{-60y}+9\)
9. \((y+11)(y+11)=(y+11)^2=y^2+\color{magenta}{2.y.11}+11^2=y^2\color{magenta}{+22y}+121\)
10. \((s+15)(s+15)=(s+15)^2=s^2+\color{magenta}{2.s.15}+15^2=s^2\color{magenta}{+30s}+225\)
11. \((4y^3-5)(4y^3-5)=(4y^3-5)^2=(4y^3)^2\color{magenta}{+2.(4y^3).(-5)}+(-5)^2=16y^{6}\color{magenta}{-40y^3}+25\)
12. \((\color{blue}{b}\color{red}{+14})(\color{blue}{b}\color{red}{-14})=\color{blue}{b}^2-\color{red}{14}^2=b^2-196\)