Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{blue}{a}\color{red}{-15})(\color{blue}{a}\color{red}{+15})=\color{blue}{a}^2-\color{red}{15}^2=a^2-225\)
2. \((16s-8)(16s-8)=(16s-8)^2=(16s)^2+\color{magenta}{2.(16s).(-8)}+(-8)^2=256s^2\color{magenta}{-256s}+64\)
3. \((\color{red}{11p}\color{blue}{+15})(\color{red}{-11p}\color{blue}{+15})=\color{blue}{15}^2-\color{red}{(11p)}^2=225-121p^2\)
4. \((p+12)^2=p^2+\color{magenta}{2.p.12}+12^2=p^2\color{magenta}{+24p}+144\)
5. \((-7x-8)^2=(-7x)^2+\color{magenta}{2.(-7x).(-8)}+(-8)^2=49x^2\color{magenta}{+112x}+64\)
6. \((3x-15)(3x-15)=(3x-15)^2=(3x)^2+\color{magenta}{2.(3x).(-15)}+(-15)^2=9x^2\color{magenta}{-90x}+225\)
7. \((\color{blue}{a}\color{red}{+6})(\color{blue}{a}\color{red}{-6})=\color{blue}{a}^2-\color{red}{6}^2=a^2-36\)
8. \((\color{red}{q^3}\color{blue}{-12})(\color{red}{-q^3}\color{blue}{-12})=\color{blue}{(-12)}^2-\color{red}{(q^3)}^2=144-q^{6}\)
9. \((p+15)^2=p^2+\color{magenta}{2.p.15}+15^2=p^2\color{magenta}{+30p}+225\)
10. \((-7a-13)(-7a-13)=(-7a-13)^2=(-7a)^2+\color{magenta}{2.(-7a).(-13)}+(-13)^2=49a^2\color{magenta}{+182a}+169\)
11. \((\color{red}{-6x}\color{blue}{+12})(\color{red}{6x}\color{blue}{+12})=\color{blue}{12}^2-\color{red}{(6x)}^2=144-36x^2\)
12. \((-8s+1)^2=(-8s)^2+\color{magenta}{2.(-8s).1}+1^2=64s^2\color{magenta}{-16s}+1\)