Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{blue}{15p^4}\color{red}{+10q})(\color{blue}{15p^4}\color{red}{-10q})=\color{blue}{(15p^4)}^2-\color{red}{(10q)}^2=225p^{8}-100q^2\)
2. \((\color{blue}{x}\color{red}{+14})(\color{blue}{x}\color{red}{-14})=\color{blue}{x}^2-\color{red}{14}^2=x^2-196\)
3. \((10y^5-13)^2=(10y^5)^2\color{magenta}{+2.(10y^5).(-13)}+(-13)^2=100y^{10}\color{magenta}{-260y^5}+169\)
4. \((5b-14)^2=(5b)^2+\color{magenta}{2.(5b).(-14)}+(-14)^2=25b^2\color{magenta}{-140b}+196\)
5. \((6b^5+13)^2=(6b^5)^2\color{magenta}{+2.(6b^5).13}+13^2=36b^{10}\color{magenta}{+156b^5}+169\)
6. \((\color{red}{6x^4}\color{blue}{-3s})(\color{red}{-6x^4}\color{blue}{-3s})=\color{blue}{(-3s)}^2-\color{red}{(6x^4)}^2=9s^2-36x^{8}\)
7. \((s-3)(s-3)=(s-3)^2=s^2+\color{magenta}{2.s.(-3)}+(-3)^2=s^2\color{magenta}{-6s}+9\)
8. \((-3p^2-11)^2=(-3p^2)^2\color{magenta}{+2.(-3p^2).(-11)}+(-11)^2=9p^{4}\color{magenta}{+66p^2}+121\)
9. \((\color{blue}{-15p}\color{red}{-2})(\color{blue}{-15p}\color{red}{+2})=\color{blue}{(-15p)}^2-\color{red}{(-2)}^2=225p^2-4\)
10. \((16x^4-14b)^2=(16x^4)^2\color{magenta}{+2.(16x^4).(-14b)}+(-14b)^2=256x^{8}\color{magenta}{-448bx^4}+196b^2\)
11. \((\color{red}{-10x}\color{blue}{+2})(\color{red}{10x}\color{blue}{+2})=\color{blue}{2}^2-\color{red}{(10x)}^2=4-100x^2\)
12. \((\color{blue}{-12a}\color{red}{+15})(\color{blue}{-12a}\color{red}{-15})=\color{blue}{(-12a)}^2-\color{red}{(15)}^2=144a^2-225\)