Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((4p^4-16q)(4p^4-16q)=(4p^4-16q)^2=(4p^4)^2\color{magenta}{+2.(4p^4).(-16q)}+(-16q)^2=16p^{8}\color{magenta}{-128p^4q}+256q^2\)
2. \((\color{blue}{b}\color{red}{-15})(\color{blue}{b}\color{red}{+15})=\color{blue}{b}^2-\color{red}{15}^2=b^2-225\)
3. \((\color{blue}{7q}\color{red}{+9})(\color{blue}{7q}\color{red}{-9})=\color{blue}{(7q)}^2-\color{red}{(9)}^2=49q^2-81\)
4. \((\color{blue}{14a}\color{red}{+14})(\color{blue}{14a}\color{red}{-14})=\color{blue}{(14a)}^2-\color{red}{(14)}^2=196a^2-196\)
5. \((-b^2-12y)^2=(-b^2)^2\color{magenta}{+2.(-b^2).(-12y)}+(-12y)^2=b^{4}\color{magenta}{+24b^2y}+144y^2\)
6. \((11s-1)^2=(11s)^2+\color{magenta}{2.(11s).(-1)}+(-1)^2=121s^2\color{magenta}{-22s}+1\)
7. \((-16x^3+14p)^2=(-16x^3)^2\color{magenta}{+2.(-16x^3).(14p)}+(14p)^2=256x^{6}\color{magenta}{-448px^3}+196p^2\)
8. \((-14q^2-16)^2=(-14q^2)^2\color{magenta}{+2.(-14q^2).(-16)}+(-16)^2=196q^{4}\color{magenta}{+448q^2}+256\)
9. \((\color{blue}{y}\color{red}{+15})(\color{blue}{y}\color{red}{-15})=\color{blue}{y}^2-\color{red}{15}^2=y^2-225\)
10. \((\color{blue}{-7b}\color{red}{-3})(\color{blue}{-7b}\color{red}{+3})=\color{blue}{(-7b)}^2-\color{red}{(-3)}^2=49b^2-9\)
11. \((2a-16)(2a-16)=(2a-16)^2=(2a)^2+\color{magenta}{2.(2a).(-16)}+(-16)^2=4a^2\color{magenta}{-64a}+256\)
12. \((9p^3+10)(9p^3+10)=(9p^3+10)^2=(9p^3)^2\color{magenta}{+2.(9p^3).10}+10^2=81p^{6}\color{magenta}{+180p^3}+100\)