Merkwaardige producten (MP)

Hoofdmenu Eentje per keer  🖨

Bereken de volgende merkwaardige producten

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

---

Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((-7q-14)(-7q-14)=(-7q-14)^2=(-7q)^2+\color{magenta}{2.(-7q).(-14)}+(-14)^2=49q^2\color{magenta}{+196q}+196\)
2. \((\color{blue}{9y^3}\color{red}{-5b})(\color{blue}{9y^3}\color{red}{+5b})=\color{blue}{(9y^3)}^2-\color{red}{(-5b)}^2=81y^{6}-25b^2\)
3. \((\color{red}{3p}\color{blue}{-15})(\color{red}{-3p}\color{blue}{-15})=\color{blue}{(-15)}^2-\color{red}{(3p)}^2=225-9p^2\)
4. \((-4s^5+6)^2=(-4s^5)^2\color{magenta}{+2.(-4s^5).6}+6^2=16s^{10}\color{magenta}{-48s^5}+36\)
5. \((13q^2+14b)(13q^2+14b)=(13q^2+14b)^2=(13q^2)^2\color{magenta}{+2.(13q^2).(14b)}+(14b)^2=169q^{4}\color{magenta}{+364bq^2}+196b^2\)
6. \((p+12)^2=p^2+\color{magenta}{2.p.12}+12^2=p^2\color{magenta}{+24p}+144\)
7. \((\color{blue}{3p^2}\color{red}{-2y})(\color{blue}{3p^2}\color{red}{+2y})=\color{blue}{(3p^2)}^2-\color{red}{(-2y)}^2=9p^{4}-4y^2\)
8. \((p+15)^2=p^2+\color{magenta}{2.p.15}+15^2=p^2\color{magenta}{+30p}+225\)
9. \((\color{blue}{4q}\color{red}{-5})(\color{blue}{4q}\color{red}{+5})=\color{blue}{(4q)}^2-\color{red}{(-5)}^2=16q^2-25\)
10. \((11s^5+16p)^2=(11s^5)^2\color{magenta}{+2.(11s^5).(16p)}+(16p)^2=121s^{10}\color{magenta}{+352ps^5}+256p^2\)
11. \((\color{red}{-13y}\color{blue}{+12})(\color{red}{13y}\color{blue}{+12})=\color{blue}{12}^2-\color{red}{(13y)}^2=144-169y^2\)
12. \((10q-14)^2=(10q)^2+\color{magenta}{2.(10q).(-14)}+(-14)^2=100q^2\color{magenta}{-280q}+196\)