Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((-12a-15)(-12a-15)=(-12a-15)^2=(-12a)^2+\color{magenta}{2.(-12a).(-15)}+(-15)^2=144a^2\color{magenta}{+360a}+225\)
2. \((14x^3-5a)(14x^3-5a)=(14x^3-5a)^2=(14x^3)^2\color{magenta}{+2.(14x^3).(-5a)}+(-5a)^2=196x^{6}\color{magenta}{-140ax^3}+25a^2\)
3. \((13b^4-14y)(13b^4-14y)=(13b^4-14y)^2=(13b^4)^2\color{magenta}{+2.(13b^4).(-14y)}+(-14y)^2=169b^{8}\color{magenta}{-364b^4y}+196y^2\)
4. \((y-11)(y-11)=(y-11)^2=y^2+\color{magenta}{2.y.(-11)}+(-11)^2=y^2\color{magenta}{-22y}+121\)
5. \((12y-3)^2=(12y)^2+\color{magenta}{2.(12y).(-3)}+(-3)^2=144y^2\color{magenta}{-72y}+9\)
6. \((-2p-14)(-2p-14)=(-2p-14)^2=(-2p)^2+\color{magenta}{2.(-2p).(-14)}+(-14)^2=4p^2\color{magenta}{+56p}+196\)
7. \((-9b^4-14p)(-9b^4-14p)=(-9b^4-14p)^2=(-9b^4)^2\color{magenta}{+2.(-9b^4).(-14p)}+(-14p)^2=81b^{8}\color{magenta}{+252b^4p}+196p^2\)
8. \((\color{blue}{y}\color{red}{-12})(\color{blue}{y}\color{red}{+12})=\color{blue}{y}^2-\color{red}{12}^2=y^2-144\)
9. \((\color{blue}{2a^4}\color{red}{-11})(\color{blue}{2a^4}\color{red}{+11})=\color{blue}{(2a^4)}^2-\color{red}{(-11)}^2=4a^{8}-121\)
10. \((\color{blue}{a}\color{red}{+11})(\color{blue}{a}\color{red}{-11})=\color{blue}{a}^2-\color{red}{11}^2=a^2-121\)
11. \((12a^3+11x)^2=(12a^3)^2\color{magenta}{+2.(12a^3).(11x)}+(11x)^2=144a^{6}\color{magenta}{+264a^3x}+121x^2\)
12. \((\color{red}{-4q^2}\color{blue}{+4p})(\color{red}{4q^2}\color{blue}{+4p})=\color{blue}{(4p)}^2-\color{red}{(4q^2)}^2=16p^2-16q^{4}\)