Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{red}{-11s^3}\color{blue}{+8q})(\color{red}{11s^3}\color{blue}{+8q})=\color{blue}{(8q)}^2-\color{red}{(11s^3)}^2=64q^2-121s^{6}\)
2. \((-3b^2-11)^2=(-3b^2)^2\color{magenta}{+2.(-3b^2).(-11)}+(-11)^2=9b^{4}\color{magenta}{+66b^2}+121\)
3. \((y+10)^2=y^2+\color{magenta}{2.y.10}+10^2=y^2\color{magenta}{+20y}+100\)
4. \((10b+14)(10b+14)=(10b+14)^2=(10b)^2+\color{magenta}{2.(10b).14}+14^2=100b^2\color{magenta}{+280b}+196\)
5. \((\color{blue}{5p^2}\color{red}{-6})(\color{blue}{5p^2}\color{red}{+6})=\color{blue}{(5p^2)}^2-\color{red}{(-6)}^2=25p^{4}-36\)
6. \((\color{red}{-16s^2}\color{blue}{+x})(\color{red}{16s^2}\color{blue}{+x})=\color{blue}{(1x)}^2-\color{red}{(16s^2)}^2=1x^2-256s^{4}\)
7. \((\color{blue}{p}\color{red}{+2})(\color{blue}{p}\color{red}{-2})=\color{blue}{p}^2-\color{red}{2}^2=p^2-4\)
8. \((\color{red}{12y^5}\color{blue}{-13})(\color{red}{-12y^5}\color{blue}{-13})=\color{blue}{(-13)}^2-\color{red}{(12y^5)}^2=169-144y^{10}\)
9. \((\color{blue}{-14y^4}\color{red}{-2a})(\color{blue}{-14y^4}\color{red}{+2a})=\color{blue}{(-14y^4)}^2-\color{red}{(-2a)}^2=196y^{8}-4a^2\)
10. \((12y^2-9b)(12y^2-9b)=(12y^2-9b)^2=(12y^2)^2\color{magenta}{+2.(12y^2).(-9b)}+(-9b)^2=144y^{4}\color{magenta}{-216by^2}+81b^2\)
11. \((12q-14)(12q-14)=(12q-14)^2=(12q)^2+\color{magenta}{2.(12q).(-14)}+(-14)^2=144q^2\color{magenta}{-336q}+196\)
12. \((12y^4-3s)^2=(12y^4)^2\color{magenta}{+2.(12y^4).(-3s)}+(-3s)^2=144y^{8}\color{magenta}{-72sy^4}+9s^2\)