Merkwaardige producten (MP)

Hoofdmenu Eentje per keer  🖨

Bereken de volgende merkwaardige producten

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

---

Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((16a^2+10)^2=(16a^2)^2\color{magenta}{+2.(16a^2).10}+10^2=256a^{4}\color{magenta}{+320a^2}+100\)
2. \((q+2)^2=q^2+\color{magenta}{2.q.2}+2^2=q^2\color{magenta}{+4q}+4\)
3. \((\color{blue}{x}\color{red}{+12})(\color{blue}{x}\color{red}{-12})=\color{blue}{x}^2-\color{red}{12}^2=x^2-144\)
4. \((\color{blue}{x}\color{red}{-15})(\color{blue}{x}\color{red}{+15})=\color{blue}{x}^2-\color{red}{15}^2=x^2-225\)
5. \((-5s^4-4y)^2=(-5s^4)^2\color{magenta}{+2.(-5s^4).(-4y)}+(-4y)^2=25s^{8}\color{magenta}{+40s^4y}+16y^2\)
6. \((15s^5-y)^2=(15s^5)^2\color{magenta}{+2.(15s^5).(-y)}+(-y)^2=225s^{10}\color{magenta}{-30s^5y}+1y^2\)
7. \((a-11)^2=a^2+\color{magenta}{2.a.(-11)}+(-11)^2=a^2\color{magenta}{-22a}+121\)
8. \((\color{red}{-7x^2}\color{blue}{+4a})(\color{red}{7x^2}\color{blue}{+4a})=\color{blue}{(4a)}^2-\color{red}{(7x^2)}^2=16a^2-49x^{4}\)
9. \((\color{red}{-16q}\color{blue}{+5})(\color{red}{16q}\color{blue}{+5})=\color{blue}{5}^2-\color{red}{(16q)}^2=25-256q^2\)
10. \((-6a^2+15)(-6a^2+15)=(-6a^2+15)^2=(-6a^2)^2\color{magenta}{+2.(-6a^2).15}+15^2=36a^{4}\color{magenta}{-180a^2}+225\)
11. \((8b^4-14q)^2=(8b^4)^2\color{magenta}{+2.(8b^4).(-14q)}+(-14q)^2=64b^{8}\color{magenta}{-224b^4q}+196q^2\)
12. \((q-2)(q-2)=(q-2)^2=q^2+\color{magenta}{2.q.(-2)}+(-2)^2=q^2\color{magenta}{-4q}+4\)