Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{blue}{4y^5}\color{red}{+3q})(\color{blue}{4y^5}\color{red}{-3q})=\color{blue}{(4y^5)}^2-\color{red}{(3q)}^2=16y^{10}-9q^2\)
2. \((15a^2-4)(15a^2-4)=(15a^2-4)^2=(15a^2)^2\color{magenta}{+2.(15a^2).(-4)}+(-4)^2=225a^{4}\color{magenta}{-120a^2}+16\)
3. \((\color{red}{5s}\color{blue}{-16})(\color{red}{-5s}\color{blue}{-16})=\color{blue}{(-16)}^2-\color{red}{(5s)}^2=256-25s^2\)
4. \((\color{blue}{11y^4}\color{red}{-7})(\color{blue}{11y^4}\color{red}{+7})=\color{blue}{(11y^4)}^2-\color{red}{(-7)}^2=121y^{8}-49\)
5. \((\color{blue}{-9q^4}\color{red}{+7x})(\color{blue}{-9q^4}\color{red}{-7x})=\color{blue}{(-9q^4)}^2-\color{red}{(7x)}^2=81q^{8}-49x^2\)
6. \((\color{red}{12y^2}\color{blue}{-11q})(\color{red}{-12y^2}\color{blue}{-11q})=\color{blue}{(-11q)}^2-\color{red}{(12y^2)}^2=121q^2-144y^{4}\)
7. \((\color{blue}{9y^4}\color{red}{-7})(\color{blue}{9y^4}\color{red}{+7})=\color{blue}{(9y^4)}^2-\color{red}{(-7)}^2=81y^{8}-49\)
8. \((-13y^2+13x)(-13y^2+13x)=(-13y^2+13x)^2=(-13y^2)^2\color{magenta}{+2.(-13y^2).(13x)}+(13x)^2=169y^{4}\color{magenta}{-338xy^2}+169x^2\)
9. \((-16p+14)^2=(-16p)^2+\color{magenta}{2.(-16p).14}+14^2=256p^2\color{magenta}{-448p}+196\)
10. \((\color{blue}{13q^5}\color{red}{-b})(\color{blue}{13q^5}\color{red}{+b})=\color{blue}{(13q^5)}^2-\color{red}{(-1b)}^2=169q^{10}-1b^2\)
11. \((-9b+1)^2=(-9b)^2+\color{magenta}{2.(-9b).1}+1^2=81b^2\color{magenta}{-18b}+1\)
12. \((\color{blue}{-12a}\color{red}{+5})(\color{blue}{-12a}\color{red}{-5})=\color{blue}{(-12a)}^2-\color{red}{(5)}^2=144a^2-25\)