Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{blue}{9q^5}\color{red}{+16y})(\color{blue}{9q^5}\color{red}{-16y})=\color{blue}{(9q^5)}^2-\color{red}{(16y)}^2=81q^{10}-256y^2\)
2. \((-p^2+4)(-p^2+4)=(-p^2+4)^2=(-p^2)^2\color{magenta}{+2.(-p^2).4}+4^2=1p^{4}\color{magenta}{-8p^2}+16\)
3. \((\color{blue}{y}\color{red}{-12})(\color{blue}{y}\color{red}{+12})=\color{blue}{y}^2-\color{red}{12}^2=y^2-144\)
4. \((-14s^2-1)(-14s^2-1)=(-14s^2-1)^2=(-14s^2)^2\color{magenta}{+2.(-14s^2).(-1)}+(-1)^2=196s^{4}\color{magenta}{+28s^2}+1\)
5. \((y-13)(y-13)=(y-13)^2=y^2+\color{magenta}{2.y.(-13)}+(-13)^2=y^2\color{magenta}{-26y}+169\)
6. \((\color{blue}{15y^2}\color{red}{+15s})(\color{blue}{15y^2}\color{red}{-15s})=\color{blue}{(15y^2)}^2-\color{red}{(15s)}^2=225y^{4}-225s^2\)
7. \((\color{blue}{x}\color{red}{-8})(\color{blue}{x}\color{red}{+8})=\color{blue}{x}^2-\color{red}{8}^2=x^2-64\)
8. \((-10a^5-14b)^2=(-10a^5)^2\color{magenta}{+2.(-10a^5).(-14b)}+(-14b)^2=100a^{10}\color{magenta}{+280a^5b}+196b^2\)
9. \((q+9)^2=q^2+\color{magenta}{2.q.9}+9^2=q^2\color{magenta}{+18q}+81\)
10. \((\color{blue}{b}\color{red}{-10})(\color{blue}{b}\color{red}{+10})=\color{blue}{b}^2-\color{red}{10}^2=b^2-100\)
11. \((\color{blue}{a}\color{red}{+13})(\color{blue}{a}\color{red}{-13})=\color{blue}{a}^2-\color{red}{13}^2=a^2-169\)
12. \((-11p^4+7)(-11p^4+7)=(-11p^4+7)^2=(-11p^4)^2\color{magenta}{+2.(-11p^4).7}+7^2=121p^{8}\color{magenta}{-154p^4}+49\)