Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{blue}{5y}\color{red}{-1})(\color{blue}{5y}\color{red}{+1})=\color{blue}{(5y)}^2-\color{red}{(-1)}^2=25y^2-1\)
2. \((-12b+6)^2=(-12b)^2+\color{magenta}{2.(-12b).6}+6^2=144b^2\color{magenta}{-144b}+36\)
3. \((b-6)(b-6)=(b-6)^2=b^2+\color{magenta}{2.b.(-6)}+(-6)^2=b^2\color{magenta}{-12b}+36\)
4. \((10y^4+11)^2=(10y^4)^2\color{magenta}{+2.(10y^4).11}+11^2=100y^{8}\color{magenta}{+220y^4}+121\)
5. \((y+8)^2=y^2+\color{magenta}{2.y.8}+8^2=y^2\color{magenta}{+16y}+64\)
6. \((\color{blue}{-10y}\color{red}{+10})(\color{blue}{-10y}\color{red}{-10})=\color{blue}{(-10y)}^2-\color{red}{(10)}^2=100y^2-100\)
7. \((\color{blue}{-15x^5}\color{red}{+16})(\color{blue}{-15x^5}\color{red}{-16})=\color{blue}{(-15x^5)}^2-\color{red}{16}^2=225x^{10}-256\)
8. \((-6q-4)^2=(-6q)^2+\color{magenta}{2.(-6q).(-4)}+(-4)^2=36q^2\color{magenta}{+48q}+16\)
9. \((\color{blue}{-7b^2}\color{red}{+12p})(\color{blue}{-7b^2}\color{red}{-12p})=\color{blue}{(-7b^2)}^2-\color{red}{(12p)}^2=49b^{4}-144p^2\)
10. \((-10b^4+16)(-10b^4+16)=(-10b^4+16)^2=(-10b^4)^2\color{magenta}{+2.(-10b^4).16}+16^2=100b^{8}\color{magenta}{-320b^4}+256\)
11. \((\color{red}{12q^2}\color{blue}{+b})(\color{red}{-12q^2}\color{blue}{+b})=\color{blue}{(1b)}^2-\color{red}{(12q^2)}^2=1b^2-144q^{4}\)
12. \((-13x^2-8b)^2=(-13x^2)^2\color{magenta}{+2.(-13x^2).(-8b)}+(-8b)^2=169x^{4}\color{magenta}{+208bx^2}+64b^2\)