Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{blue}{-12b^2}\color{red}{-13s})(\color{blue}{-12b^2}\color{red}{+13s})=\color{blue}{(-12b^2)}^2-\color{red}{(-13s)}^2=144b^{4}-169s^2\)
2. \((-2p-14)(-2p-14)=(-2p-14)^2=(-2p)^2+\color{magenta}{2.(-2p).(-14)}+(-14)^2=4p^2\color{magenta}{+56p}+196\)
3. \((\color{red}{-12a^3}\color{blue}{-11s})(\color{red}{12a^3}\color{blue}{-11s})=\color{blue}{(-11s)}^2-\color{red}{(12a^3)}^2=121s^2-144a^{6}\)
4. \((\color{blue}{12p^2}\color{red}{-10y})(\color{blue}{12p^2}\color{red}{+10y})=\color{blue}{(12p^2)}^2-\color{red}{(-10y)}^2=144p^{4}-100y^2\)
5. \((\color{blue}{y}\color{red}{+8})(\color{blue}{y}\color{red}{-8})=\color{blue}{y}^2-\color{red}{8}^2=y^2-64\)
6. \((\color{blue}{q}\color{red}{-1})(\color{blue}{q}\color{red}{+1})=\color{blue}{q}^2-\color{red}{1}^2=q^2-1\)
7. \((p+3)^2=p^2+\color{magenta}{2.p.3}+3^2=p^2\color{magenta}{+6p}+9\)
8. \((-14x^3+8q)(-14x^3+8q)=(-14x^3+8q)^2=(-14x^3)^2\color{magenta}{+2.(-14x^3).(8q)}+(8q)^2=196x^{6}\color{magenta}{-224qx^3}+64q^2\)
9. \((p^3-13)(p^3-13)=(p^3-13)^2=(p^3)^2\color{magenta}{+2.(p^3).(-13)}+(-13)^2=1p^{6}\color{magenta}{-26p^3}+169\)
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. \((b+10)(b+10)=(b+10)^2=b^2+\color{magenta}{2.b.10}+10^2=b^2\color{magenta}{+20b}+100\)
12. \((\color{red}{4q^5}\color{blue}{+3})(\color{red}{-4q^5}\color{blue}{+3})=\color{blue}{3}^2-\color{red}{(4q^5)}^2=9-16q^{10}\)