Merkwaardige producten (MP)

Hoofdmenu Eentje per keer  🖨

Bereken de volgende merkwaardige producten

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

---

Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{blue}{q}\color{red}{-2})(\color{blue}{q}\color{red}{+2})=\color{blue}{q}^2-\color{red}{2}^2=q^2-4\)
2. \((\color{red}{5y^5}\color{blue}{-4})(\color{red}{-5y^5}\color{blue}{-4})=\color{blue}{(-4)}^2-\color{red}{(5y^5)}^2=16-25y^{10}\)
3. \((12x+6)(12x+6)=(12x+6)^2=(12x)^2+\color{magenta}{2.(12x).6}+6^2=144x^2\color{magenta}{+144x}+36\)
4. \((\color{blue}{y}\color{red}{-6})(\color{blue}{y}\color{red}{+6})=\color{blue}{y}^2-\color{red}{6}^2=y^2-36\)
5. \((\color{red}{2p}\color{blue}{-7})(\color{red}{-2p}\color{blue}{-7})=\color{blue}{(-7)}^2-\color{red}{(2p)}^2=49-4p^2\)
6. \((14y^4-p)(14y^4-p)=(14y^4-p)^2=(14y^4)^2\color{magenta}{+2.(14y^4).(-p)}+(-p)^2=196y^{8}\color{magenta}{-28py^4}+1p^2\)
7. \((\color{blue}{b}\color{red}{+16})(\color{blue}{b}\color{red}{-16})=\color{blue}{(b)}^2-\color{red}{(16)}^2=b^2-256\)
8. \((3q^5-2b)^2=(3q^5)^2\color{magenta}{+2.(3q^5).(-2b)}+(-2b)^2=9q^{10}\color{magenta}{-12bq^5}+4b^2\)
9. \((b-5)(b-5)=(b-5)^2=b^2+\color{magenta}{2.b.(-5)}+(-5)^2=b^2\color{magenta}{-10b}+25\)
10. \((15s^3+6)(15s^3+6)=(15s^3+6)^2=(15s^3)^2\color{magenta}{+2.(15s^3).6}+6^2=225s^{6}\color{magenta}{+180s^3}+36\)
11. \((-10q+8)(-10q+8)=(-10q+8)^2=(-10q)^2+\color{magenta}{2.(-10q).8}+8^2=100q^2\color{magenta}{-160q}+64\)
12. \((\color{blue}{a}\color{red}{-15})(\color{blue}{a}\color{red}{+15})=\color{blue}{a}^2-\color{red}{15}^2=a^2-225\)