Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{red}{10y^3}\color{blue}{-4})(\color{red}{-10y^3}\color{blue}{-4})=\color{blue}{(-4)}^2-\color{red}{(10y^3)}^2=16-100y^{6}\)
2. \((\color{red}{4b^4}\color{blue}{+16})(\color{red}{-4b^4}\color{blue}{+16})=\color{blue}{16}^2-\color{red}{(4b^4)}^2=256-16b^{8}\)
3. \((\color{red}{13x^3}\color{blue}{+5q})(\color{red}{-13x^3}\color{blue}{+5q})=\color{blue}{(5q)}^2-\color{red}{(13x^3)}^2=25q^2-169x^{6}\)
4. \((\color{blue}{x}\color{red}{+2})(\color{blue}{x}\color{red}{-2})=\color{blue}{x}^2-\color{red}{2}^2=x^2-4\)
5. \((\color{blue}{x}\color{red}{+13})(\color{blue}{x}\color{red}{-13})=\color{blue}{x}^2-\color{red}{13}^2=x^2-169\)
6. \((\color{blue}{-12p^5}\color{red}{-16})(\color{blue}{-12p^5}\color{red}{+16})=\color{blue}{(-12p^5)}^2-\color{red}{(-16)}^2=144p^{10}-256\)
7. \((\color{blue}{-2b^4}\color{red}{-16y})(\color{blue}{-2b^4}\color{red}{+16y})=\color{blue}{(-2b^4)}^2-\color{red}{(-16y)}^2=4b^{8}-256y^2\)
8. \((\color{blue}{-b}\color{red}{-8})(\color{blue}{-b}\color{red}{+8})=\color{blue}{(-b)}^2-\color{red}{(-8)}^2=b^2-64\)
9. \((-8b^2-x)(-8b^2-x)=(-8b^2-x)^2=(-8b^2)^2\color{magenta}{+2.(-8b^2).(-x)}+(-x)^2=64b^{4}\color{magenta}{+16b^2x}+1x^2\)
10. \((a-14)^2=a^2+\color{magenta}{2.a.(-14)}+(-14)^2=a^2\color{magenta}{-28a}+196\)
11. \((s+12)^2=s^2+\color{magenta}{2.s.12}+12^2=s^2\color{magenta}{+24s}+144\)
12. \((-15a^5-7b)^2=(-15a^5)^2\color{magenta}{+2.(-15a^5).(-7b)}+(-7b)^2=225a^{10}\color{magenta}{+210a^5b}+49b^2\)