Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((15y^5+11)(15y^5+11)=(15y^5+11)^2=(15y^5)^2\color{magenta}{+2.(15y^5).11}+11^2=225y^{10}\color{magenta}{+330y^5}+121\)
2. \((16x^3-10b)^2=(16x^3)^2\color{magenta}{+2.(16x^3).(-10b)}+(-10b)^2=256x^{6}\color{magenta}{-320bx^3}+100b^2\)
3. \((-4b^4-5a)(-4b^4-5a)=(-4b^4-5a)^2=(-4b^4)^2\color{magenta}{+2.(-4b^4).(-5a)}+(-5a)^2=16b^{8}\color{magenta}{+40ab^4}+25a^2\)
4. \((s-4)(s-4)=(s-4)^2=s^2+\color{magenta}{2.s.(-4)}+(-4)^2=s^2\color{magenta}{-8s}+16\)
5. \((-3s^3+11)^2=(-3s^3)^2\color{magenta}{+2.(-3s^3).11}+11^2=9s^{6}\color{magenta}{-66s^3}+121\)
6. \((10y-6)^2=(10y)^2+\color{magenta}{2.(10y).(-6)}+(-6)^2=100y^2\color{magenta}{-120y}+36\)
7. \((\color{blue}{-15q^5}\color{red}{-14})(\color{blue}{-15q^5}\color{red}{+14})=\color{blue}{(-15q^5)}^2-\color{red}{(-14)}^2=225q^{10}-196\)
8. \((\color{blue}{-4x}\color{red}{+15})(\color{blue}{-4x}\color{red}{-15})=\color{blue}{(-4x)}^2-\color{red}{(15)}^2=16x^2-225\)
9. \((\color{blue}{7b^5}\color{red}{+6})(\color{blue}{7b^5}\color{red}{-6})=\color{blue}{(7b^5)}^2-\color{red}{6}^2=49b^{10}-36\)
10. \((\color{blue}{y}\color{red}{+11})(\color{blue}{y}\color{red}{-11})=\color{blue}{y}^2-\color{red}{11}^2=y^2-121\)
11. \((6a-13)(6a-13)=(6a-13)^2=(6a)^2+\color{magenta}{2.(6a).(-13)}+(-13)^2=36a^2\color{magenta}{-156a}+169\)
12. \((\color{red}{b}\color{blue}{-16})(\color{red}{-b}\color{blue}{-16})=\color{blue}{(-16)}^2-\color{red}{(b)}^2=256-b^2\)