Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{red}{-16x^2}\color{blue}{-11y})(\color{red}{16x^2}\color{blue}{-11y})=\color{blue}{(-11y)}^2-\color{red}{(16x^2)}^2=121y^2-256x^{4}\)
2. \((\color{red}{-13y^2}\color{blue}{+4a})(\color{red}{13y^2}\color{blue}{+4a})=\color{blue}{(4a)}^2-\color{red}{(13y^2)}^2=16a^2-169y^{4}\)
3. \((\color{red}{-14b^4}\color{blue}{+12})(\color{red}{14b^4}\color{blue}{+12})=\color{blue}{12}^2-\color{red}{(14b^4)}^2=144-196b^{8}\)
4. \((\color{blue}{-2b}\color{red}{-7})(\color{blue}{-2b}\color{red}{+7})=\color{blue}{(-2b)}^2-\color{red}{(-7)}^2=4b^2-49\)
5. \((-4x^2-7y)(-4x^2-7y)=(-4x^2-7y)^2=(-4x^2)^2\color{magenta}{+2.(-4x^2).(-7y)}+(-7y)^2=16x^{4}\color{magenta}{+56x^2y}+49y^2\)
6. \((\color{red}{-4s^5}\color{blue}{-3x})(\color{red}{4s^5}\color{blue}{-3x})=\color{blue}{(-3x)}^2-\color{red}{(4s^5)}^2=9x^2-16s^{10}\)
7. \((\color{blue}{-10s^4}\color{red}{+1})(\color{blue}{-10s^4}\color{red}{-1})=\color{blue}{(-10s^4)}^2-\color{red}{1}^2=100s^{8}-1\)
8. \((\color{red}{14b^5}\color{blue}{+7y})(\color{red}{-14b^5}\color{blue}{+7y})=\color{blue}{(7y)}^2-\color{red}{(14b^5)}^2=49y^2-196b^{10}\)
9. \((\color{blue}{x}\color{red}{+10})(\color{blue}{x}\color{red}{-10})=\color{blue}{x}^2-\color{red}{10}^2=x^2-100\)
10. \((x-2)^2=x^2+\color{magenta}{2.x.(-2)}+(-2)^2=x^2\color{magenta}{-4x}+4\)
11. \((-16s^5-9)^2=(-16s^5)^2\color{magenta}{+2.(-16s^5).(-9)}+(-9)^2=256s^{10}\color{magenta}{+288s^5}+81\)
12. \((\color{blue}{b}\color{red}{+12})(\color{blue}{b}\color{red}{-12})=\color{blue}{b}^2-\color{red}{12}^2=b^2-144\)