Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((a+5)^2=a^2+\color{magenta}{2.a.5}+5^2=a^2\color{magenta}{+10a}+25\)
2. \((\color{blue}{-6q}\color{red}{+14})(\color{blue}{-6q}\color{red}{-14})=\color{blue}{(-6q)}^2-\color{red}{(14)}^2=36q^2-196\)
3. \((15q^2+9p)(15q^2+9p)=(15q^2+9p)^2=(15q^2)^2\color{magenta}{+2.(15q^2).(9p)}+(9p)^2=225q^{4}\color{magenta}{+270pq^2}+81p^2\)
4. \((8s-15)(8s-15)=(8s-15)^2=(8s)^2+\color{magenta}{2.(8s).(-15)}+(-15)^2=64s^2\color{magenta}{-240s}+225\)
5. \((15y-16)(15y-16)=(15y-16)^2=(15y)^2+\color{magenta}{2.(15y).(-16)}+(-16)^2=225y^2\color{magenta}{-480y}+256\)
6. \((-a^5+7)(-a^5+7)=(-a^5+7)^2=(-a^5)^2\color{magenta}{+2.(-a^5).7}+7^2=1a^{10}\color{magenta}{-14a^5}+49\)
7. \((\color{red}{-s}\color{blue}{-15})(\color{red}{s}\color{blue}{-15})=\color{blue}{(-15)}^2-\color{red}{(s)}^2=225-s^2\)
8. \((5a^3-7p)^2=(5a^3)^2\color{magenta}{+2.(5a^3).(-7p)}+(-7p)^2=25a^{6}\color{magenta}{-70a^3p}+49p^2\)
9. \((\color{red}{11a}\color{blue}{-7})(\color{red}{-11a}\color{blue}{-7})=\color{blue}{(-7)}^2-\color{red}{(11a)}^2=49-121a^2\)
10. \((2b^4+9q)(2b^4+9q)=(2b^4+9q)^2=(2b^4)^2\color{magenta}{+2.(2b^4).(9q)}+(9q)^2=4b^{8}\color{magenta}{+36b^4q}+81q^2\)
11. \((b-9)(b-9)=(b-9)^2=b^2+\color{magenta}{2.b.(-9)}+(-9)^2=b^2\color{magenta}{-18b}+81\)
12. \((9b+14)(9b+14)=(9b+14)^2=(9b)^2+\color{magenta}{2.(9b).14}+14^2=81b^2\color{magenta}{+252b}+196\)