Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{red}{9p^3}\color{blue}{-13y})(\color{red}{-9p^3}\color{blue}{-13y})=\color{blue}{(-13y)}^2-\color{red}{(9p^3)}^2=169y^2-81p^{6}\)
2. \((\color{red}{5p^4}\color{blue}{-11})(\color{red}{-5p^4}\color{blue}{-11})=\color{blue}{(-11)}^2-\color{red}{(5p^4)}^2=121-25p^{8}\)
3. \((x^3+10)^2=(x^3)^2\color{magenta}{+2.(x^3).10}+10^2=1x^{6}\color{magenta}{+20x^3}+100\)
4. \((-9y^4-16)(-9y^4-16)=(-9y^4-16)^2=(-9y^4)^2\color{magenta}{+2.(-9y^4).(-16)}+(-16)^2=81y^{8}\color{magenta}{+288y^4}+256\)
5. \((q-5)^2=q^2+\color{magenta}{2.q.(-5)}+(-5)^2=q^2\color{magenta}{-10q}+25\)
6. \((p+3)^2=p^2+\color{magenta}{2.p.3}+3^2=p^2\color{magenta}{+6p}+9\)
7. \((\color{blue}{-11x^4}\color{red}{+15a})(\color{blue}{-11x^4}\color{red}{-15a})=\color{blue}{(-11x^4)}^2-\color{red}{(15a)}^2=121x^{8}-225a^2\)
8. \((b+4)^2=(b)^2+\color{magenta}{2.(b).4}+4^2=b^2\color{magenta}{+8b}+16\)
9. \((\color{red}{13s^3}\color{blue}{+6})(\color{red}{-13s^3}\color{blue}{+6})=\color{blue}{6}^2-\color{red}{(13s^3)}^2=36-169s^{6}\)
10. \((\color{blue}{-14s}\color{red}{-2})(\color{blue}{-14s}\color{red}{+2})=\color{blue}{(-14s)}^2-\color{red}{(-2)}^2=196s^2-4\)
11. \((\color{red}{-7b^3}\color{blue}{-10})(\color{red}{7b^3}\color{blue}{-10})=\color{blue}{(-10)}^2-\color{red}{(7b^3)}^2=100-49b^{6}\)
12. \((\color{red}{-15s^4}\color{blue}{-10a})(\color{red}{15s^4}\color{blue}{-10a})=\color{blue}{(-10a)}^2-\color{red}{(15s^4)}^2=100a^2-225s^{8}\)