Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{blue}{p}\color{red}{-1})(\color{blue}{p}\color{red}{+1})=\color{blue}{p}^2-\color{red}{1}^2=p^2-1\)
2. \((-12b+15)^2=(-12b)^2+\color{magenta}{2.(-12b).15}+15^2=144b^2\color{magenta}{-360b}+225\)
3. \((-7p^3-8s)^2=(-7p^3)^2\color{magenta}{+2.(-7p^3).(-8s)}+(-8s)^2=49p^{6}\color{magenta}{+112p^3s}+64s^2\)
4. \((b-14)^2=b^2+\color{magenta}{2.b.(-14)}+(-14)^2=b^2\color{magenta}{-28b}+196\)
5. \((\color{blue}{x}\color{red}{-15})(\color{blue}{x}\color{red}{+15})=\color{blue}{x}^2-\color{red}{15}^2=x^2-225\)
6. \((-5x+10)^2=(-5x)^2+\color{magenta}{2.(-5x).10}+10^2=25x^2\color{magenta}{-100x}+100\)
7. \((\color{red}{b^4}\color{blue}{-3})(\color{red}{-b^4}\color{blue}{-3})=\color{blue}{(-3)}^2-\color{red}{(b^4)}^2=9-b^{8}\)
8. \((\color{blue}{7b}\color{red}{-1})(\color{blue}{7b}\color{red}{+1})=\color{blue}{(7b)}^2-\color{red}{(-1)}^2=49b^2-1\)
9. \((2a^4+2)^2=(2a^4)^2\color{magenta}{+2.(2a^4).2}+2^2=4a^{8}\color{magenta}{+8a^4}+4\)
10. \((\color{red}{-13a}\color{blue}{-1})(\color{red}{13a}\color{blue}{-1})=\color{blue}{(-1)}^2-\color{red}{(13a)}^2=1-169a^2\)
11. \((\color{red}{4y^5}\color{blue}{+3s})(\color{red}{-4y^5}\color{blue}{+3s})=\color{blue}{(3s)}^2-\color{red}{(4y^5)}^2=9s^2-16y^{10}\)
12. \((\color{blue}{q}\color{red}{-9})(\color{blue}{q}\color{red}{+9})=\color{blue}{q}^2-\color{red}{9}^2=q^2-81\)