Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((2p^2-10)^2=(2p^2)^2\color{magenta}{+2.(2p^2).(-10)}+(-10)^2=4p^{4}\color{magenta}{-40p^2}+100\)
2. \((p+3)^2=p^2+\color{magenta}{2.p.3}+3^2=p^2\color{magenta}{+6p}+9\)
3. \((11y^5+8)(11y^5+8)=(11y^5+8)^2=(11y^5)^2\color{magenta}{+2.(11y^5).8}+8^2=121y^{10}\color{magenta}{+176y^5}+64\)
4. \((s+11)(s+11)=(s+11)^2=(s)^2+\color{magenta}{2.(s).11}+11^2=s^2\color{magenta}{+22s}+121\)
5. \((\color{blue}{-4s^3}\color{red}{+14p})(\color{blue}{-4s^3}\color{red}{-14p})=\color{blue}{(-4s^3)}^2-\color{red}{(14p)}^2=16s^{6}-196p^2\)
6. \((q-6)(q-6)=(q-6)^2=q^2+\color{magenta}{2.q.(-6)}+(-6)^2=q^2\color{magenta}{-12q}+36\)
7. \((\color{blue}{-6x}\color{red}{+13})(\color{blue}{-6x}\color{red}{-13})=\color{blue}{(-6x)}^2-\color{red}{(13)}^2=36x^2-169\)
8. \((11b^3-6x)^2=(11b^3)^2\color{magenta}{+2.(11b^3).(-6x)}+(-6x)^2=121b^{6}\color{magenta}{-132b^3x}+36x^2\)
9. \((-14y^4-9)(-14y^4-9)=(-14y^4-9)^2=(-14y^4)^2\color{magenta}{+2.(-14y^4).(-9)}+(-9)^2=196y^{8}\color{magenta}{+252y^4}+81\)
10. \((\color{red}{-9a}\color{blue}{-9})(\color{red}{9a}\color{blue}{-9})=\color{blue}{(-9)}^2-\color{red}{(9a)}^2=81-81a^2\)
11. \((-8p^5-8)(-8p^5-8)=(-8p^5-8)^2=(-8p^5)^2\color{magenta}{+2.(-8p^5).(-8)}+(-8)^2=64p^{10}\color{magenta}{+128p^5}+64\)
12. \((14s+5)(14s+5)=(14s+5)^2=(14s)^2+\color{magenta}{2.(14s).5}+5^2=196s^2\color{magenta}{+140s}+25\)