Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((8y^3+7)^2=(8y^3)^2\color{magenta}{+2.(8y^3).7}+7^2=64y^{6}\color{magenta}{+112y^3}+49\)
2. \((\color{blue}{y}\color{red}{+9})(\color{blue}{y}\color{red}{-9})=\color{blue}{y}^2-\color{red}{9}^2=y^2-81\)
3. \((13p^5-16x)(13p^5-16x)=(13p^5-16x)^2=(13p^5)^2\color{magenta}{+2.(13p^5).(-16x)}+(-16x)^2=169p^{10}\color{magenta}{-416p^5x}+256x^2\)
4. \((\color{blue}{-11b^4}\color{red}{-12a})(\color{blue}{-11b^4}\color{red}{+12a})=\color{blue}{(-11b^4)}^2-\color{red}{(-12a)}^2=121b^{8}-144a^2\)
5. \((p-8)^2=p^2+\color{magenta}{2.p.(-8)}+(-8)^2=p^2\color{magenta}{-16p}+64\)
6. \((-6p^4+12y)(-6p^4+12y)=(-6p^4+12y)^2=(-6p^4)^2\color{magenta}{+2.(-6p^4).(12y)}+(12y)^2=36p^{8}\color{magenta}{-144p^4y}+144y^2\)
7. \((s-2)(s-2)=(s-2)^2=s^2+\color{magenta}{2.s.(-2)}+(-2)^2=s^2\color{magenta}{-4s}+4\)
8. \((\color{blue}{p}\color{red}{+1})(\color{blue}{p}\color{red}{-1})=\color{blue}{p}^2-\color{red}{1}^2=p^2-1\)
9. \((\color{blue}{5b}\color{red}{+6})(\color{blue}{5b}\color{red}{-6})=\color{blue}{(5b)}^2-\color{red}{(6)}^2=25b^2-36\)
10. \((9x^2-10)^2=(9x^2)^2\color{magenta}{+2.(9x^2).(-10)}+(-10)^2=81x^{4}\color{magenta}{-180x^2}+100\)
11. \((x+6)^2=x^2+\color{magenta}{2.x.6}+6^2=x^2\color{magenta}{+12x}+36\)
12. \((3q+13)(3q+13)=(3q+13)^2=(3q)^2+\color{magenta}{2.(3q).13}+13^2=9q^2\color{magenta}{+78q}+169\)