Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((-5s+10)^2=(-5s)^2+\color{magenta}{2.(-5s).10}+10^2=25s^2\color{magenta}{-100s}+100\)
2. \((\color{blue}{-10y}\color{red}{-15})(\color{blue}{-10y}\color{red}{+15})=\color{blue}{(-10y)}^2-\color{red}{(-15)}^2=100y^2-225\)
3. \((-14y+1)^2=(-14y)^2+\color{magenta}{2.(-14y).1}+1^2=196y^2\color{magenta}{-28y}+1\)
4. \((x-13)^2=x^2+\color{magenta}{2.x.(-13)}+(-13)^2=x^2\color{magenta}{-26x}+169\)
5. \((-2p^4-11a)(-2p^4-11a)=(-2p^4-11a)^2=(-2p^4)^2\color{magenta}{+2.(-2p^4).(-11a)}+(-11a)^2=4p^{8}\color{magenta}{+44ap^4}+121a^2\)
6. \((\color{red}{16q^2}\color{blue}{-s})(\color{red}{-16q^2}\color{blue}{-s})=\color{blue}{(-1s)}^2-\color{red}{(16q^2)}^2=1s^2-256q^{4}\)
7. \((4a^4+1)^2=(4a^4)^2\color{magenta}{+2.(4a^4).1}+1^2=16a^{8}\color{magenta}{+8a^4}+1\)
8. \((b-4)(b-4)=(b-4)^2=b^2+\color{magenta}{2.b.(-4)}+(-4)^2=b^2\color{magenta}{-8b}+16\)
9. \((7x^2-1)^2=(7x^2)^2\color{magenta}{+2.(7x^2).(-1)}+(-1)^2=49x^{4}\color{magenta}{-14x^2}+1\)
10. \((\color{blue}{-3b}\color{red}{-5})(\color{blue}{-3b}\color{red}{+5})=\color{blue}{(-3b)}^2-\color{red}{(-5)}^2=9b^2-25\)
11. \((\color{blue}{15a^2}\color{red}{-15})(\color{blue}{15a^2}\color{red}{+15})=\color{blue}{(15a^2)}^2-\color{red}{(-15)}^2=225a^{4}-225\)
12. \((\color{blue}{10b}\color{red}{-15})(\color{blue}{10b}\color{red}{+15})=\color{blue}{(10b)}^2-\color{red}{(-15)}^2=100b^2-225\)