Merkwaardige producten (MP)

Hoofdmenu Eentje per keer  🖨

Bereken de volgende merkwaardige producten

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

---

Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{blue}{x}\color{red}{-12})(\color{blue}{x}\color{red}{+12})=\color{blue}{x}^2-\color{red}{12}^2=x^2-144\)
2. \((\color{blue}{-3y^4}\color{red}{+12})(\color{blue}{-3y^4}\color{red}{-12})=\color{blue}{(-3y^4)}^2-\color{red}{12}^2=9y^{8}-144\)
3. \((\color{blue}{6x^4}\color{red}{+13b})(\color{blue}{6x^4}\color{red}{-13b})=\color{blue}{(6x^4)}^2-\color{red}{(13b)}^2=36x^{8}-169b^2\)
4. \((2s^2-5p)(2s^2-5p)=(2s^2-5p)^2=(2s^2)^2\color{magenta}{+2.(2s^2).(-5p)}+(-5p)^2=4s^{4}\color{magenta}{-20ps^2}+25p^2\)
5. \((\color{blue}{a}\color{red}{+15})(\color{blue}{a}\color{red}{-15})=\color{blue}{a}^2-\color{red}{15}^2=a^2-225\)
6. \((-10p-14)(-10p-14)=(-10p-14)^2=(-10p)^2+\color{magenta}{2.(-10p).(-14)}+(-14)^2=100p^2\color{magenta}{+280p}+196\)
7. \((-2p+9)(-2p+9)=(-2p+9)^2=(-2p)^2+\color{magenta}{2.(-2p).9}+9^2=4p^2\color{magenta}{-36p}+81\)
8. \((\color{red}{-13y^4}\color{blue}{+15p})(\color{red}{13y^4}\color{blue}{+15p})=\color{blue}{(15p)}^2-\color{red}{(13y^4)}^2=225p^2-169y^{8}\)
9. \((y-7)(y-7)=(y-7)^2=y^2+\color{magenta}{2.y.(-7)}+(-7)^2=y^2\color{magenta}{-14y}+49\)
10. \((\color{blue}{6s}\color{red}{+8})(\color{blue}{6s}\color{red}{-8})=\color{blue}{(6s)}^2-\color{red}{(8)}^2=36s^2-64\)
11. \((\color{blue}{-2a}\color{red}{+10})(\color{blue}{-2a}\color{red}{-10})=\color{blue}{(-2a)}^2-\color{red}{(10)}^2=4a^2-100\)
12. \((\color{red}{-6a}\color{blue}{+4})(\color{red}{6a}\color{blue}{+4})=\color{blue}{4}^2-\color{red}{(6a)}^2=16-36a^2\)