Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((3b+16)^2=(3b)^2+\color{magenta}{2.(3b).16}+16^2=9b^2\color{magenta}{+96b}+256\)
2. \((-5b^4+16)(-5b^4+16)=(-5b^4+16)^2=(-5b^4)^2\color{magenta}{+2.(-5b^4).16}+16^2=25b^{8}\color{magenta}{-160b^4}+256\)
3. \((5b^5+8y)^2=(5b^5)^2\color{magenta}{+2.(5b^5).(8y)}+(8y)^2=25b^{10}\color{magenta}{+80b^5y}+64y^2\)
4. \((\color{blue}{s^3}\color{red}{-11p})(\color{blue}{s^3}\color{red}{+11p})=\color{blue}{(s^3)}^2-\color{red}{(-11p)}^2=s^{6}-121p^2\)
5. \((q-14)^2=q^2+\color{magenta}{2.q.(-14)}+(-14)^2=q^2\color{magenta}{-28q}+196\)
6. \((b-11)^2=b^2+\color{magenta}{2.b.(-11)}+(-11)^2=b^2\color{magenta}{-22b}+121\)
7. \((q+13)(q+13)=(q+13)^2=q^2+\color{magenta}{2.q.13}+13^2=q^2\color{magenta}{+26q}+169\)
8. \((\color{blue}{6b^4}\color{red}{+1})(\color{blue}{6b^4}\color{red}{-1})=\color{blue}{(6b^4)}^2-\color{red}{1}^2=36b^{8}-1\)
9. \((8b^5-14)^2=(8b^5)^2\color{magenta}{+2.(8b^5).(-14)}+(-14)^2=64b^{10}\color{magenta}{-224b^5}+196\)
10. \((-11a^3+5)^2=(-11a^3)^2\color{magenta}{+2.(-11a^3).5}+5^2=121a^{6}\color{magenta}{-110a^3}+25\)
11. \((-4x-15)(-4x-15)=(-4x-15)^2=(-4x)^2+\color{magenta}{2.(-4x).(-15)}+(-15)^2=16x^2\color{magenta}{+120x}+225\)
12. \((-16y^2-16p)(-16y^2-16p)=(-16y^2-16p)^2=(-16y^2)^2\color{magenta}{+2.(-16y^2).(-16p)}+(-16p)^2=256y^{4}\color{magenta}{+512py^2}+256p^2\)