Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{blue}{14y^2}\color{red}{+13x})(\color{blue}{14y^2}\color{red}{-13x})=\color{blue}{(14y^2)}^2-\color{red}{(13x)}^2=196y^{4}-169x^2\)
2. \((-8q^3-3)(-8q^3-3)=(-8q^3-3)^2=(-8q^3)^2\color{magenta}{+2.(-8q^3).(-3)}+(-3)^2=64q^{6}\color{magenta}{+48q^3}+9\)
3. \((14s+10)(14s+10)=(14s+10)^2=(14s)^2+\color{magenta}{2.(14s).10}+10^2=196s^2\color{magenta}{+280s}+100\)
4. \((8y+11)^2=(8y)^2+\color{magenta}{2.(8y).11}+11^2=64y^2\color{magenta}{+176y}+121\)
5. \((\color{blue}{-b^2}\color{red}{-6})(\color{blue}{-b^2}\color{red}{+6})=\color{blue}{(-b^2)}^2-\color{red}{(-6)}^2=b^{4}-36\)
6. \((5b^3+5)^2=(5b^3)^2\color{magenta}{+2.(5b^3).5}+5^2=25b^{6}\color{magenta}{+50b^3}+25\)
7. \((a-7)^2=a^2+\color{magenta}{2.a.(-7)}+(-7)^2=a^2\color{magenta}{-14a}+49\)
8. \((6x^3-14q)^2=(6x^3)^2\color{magenta}{+2.(6x^3).(-14q)}+(-14q)^2=36x^{6}\color{magenta}{-168qx^3}+196q^2\)
9. \((-5x^2+12b)(-5x^2+12b)=(-5x^2+12b)^2=(-5x^2)^2\color{magenta}{+2.(-5x^2).(12b)}+(12b)^2=25x^{4}\color{magenta}{-120bx^2}+144b^2\)
10. \((\color{blue}{s}\color{red}{+5})(\color{blue}{s}\color{red}{-5})=\color{blue}{s}^2-\color{red}{5}^2=s^2-25\)
11. \((5b^2+s)(5b^2+s)=(5b^2+s)^2=(5b^2)^2\color{magenta}{+2.(5b^2).(s)}+(s)^2=25b^{4}\color{magenta}{+10b^2s}+1s^2\)
12. \((11b+6)^2=(11b)^2+\color{magenta}{2.(11b).6}+6^2=121b^2\color{magenta}{+132b}+36\)