Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((-8q+12)^2=(-8q)^2+\color{magenta}{2.(-8q).12}+12^2=64q^2\color{magenta}{-192q}+144\)
2. \((\color{blue}{y}\color{red}{+5})(\color{blue}{y}\color{red}{-5})=\color{blue}{y}^2-\color{red}{5}^2=y^2-25\)
3. \((\color{blue}{12s}\color{red}{+8})(\color{blue}{12s}\color{red}{-8})=\color{blue}{(12s)}^2-\color{red}{(8)}^2=144s^2-64\)
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. \((\color{red}{-3a}\color{blue}{+5})(\color{red}{3a}\color{blue}{+5})=\color{blue}{5}^2-\color{red}{(3a)}^2=25-9a^2\)
6. \((4x^2-9y)^2=(4x^2)^2\color{magenta}{+2.(4x^2).(-9y)}+(-9y)^2=16x^{4}\color{magenta}{-72x^2y}+81y^2\)
7. \((6q^3-7)^2=(6q^3)^2\color{magenta}{+2.(6q^3).(-7)}+(-7)^2=36q^{6}\color{magenta}{-84q^3}+49\)
8. \((-15p^5-13)(-15p^5-13)=(-15p^5-13)^2=(-15p^5)^2\color{magenta}{+2.(-15p^5).(-13)}+(-13)^2=225p^{10}\color{magenta}{+390p^5}+169\)
9. \((-10p^4-5b)(-10p^4-5b)=(-10p^4-5b)^2=(-10p^4)^2\color{magenta}{+2.(-10p^4).(-5b)}+(-5b)^2=100p^{8}\color{magenta}{+100bp^4}+25b^2\)
10. \((-16a-3)(-16a-3)=(-16a-3)^2=(-16a)^2+\color{magenta}{2.(-16a).(-3)}+(-3)^2=256a^2\color{magenta}{+96a}+9\)
11. \((\color{blue}{p}\color{red}{+11})(\color{blue}{p}\color{red}{-11})=\color{blue}{p}^2-\color{red}{11}^2=p^2-121\)
12. \((\color{blue}{-12x^5}\color{red}{+3})(\color{blue}{-12x^5}\color{red}{-3})=\color{blue}{(-12x^5)}^2-\color{red}{3}^2=144x^{10}-9\)