Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{blue}{6q^2}\color{red}{+9s})(\color{blue}{6q^2}\color{red}{-9s})=\color{blue}{(6q^2)}^2-\color{red}{(9s)}^2=36q^{4}-81s^2\)
2. \((\color{blue}{-8s^2}\color{red}{-4x})(\color{blue}{-8s^2}\color{red}{+4x})=\color{blue}{(-8s^2)}^2-\color{red}{(-4x)}^2=64s^{4}-16x^2\)
3. \((10a^5+2x)(10a^5+2x)=(10a^5+2x)^2=(10a^5)^2\color{magenta}{+2.(10a^5).(2x)}+(2x)^2=100a^{10}\color{magenta}{+40a^5x}+4x^2\)
4. \((-7s-3)(-7s-3)=(-7s-3)^2=(-7s)^2+\color{magenta}{2.(-7s).(-3)}+(-3)^2=49s^2\color{magenta}{+42s}+9\)
5. \((5q^4-4b)(5q^4-4b)=(5q^4-4b)^2=(5q^4)^2\color{magenta}{+2.(5q^4).(-4b)}+(-4b)^2=25q^{8}\color{magenta}{-40bq^4}+16b^2\)
6. \((-6y+13)^2=(-6y)^2+\color{magenta}{2.(-6y).13}+13^2=36y^2\color{magenta}{-156y}+169\)
7. \((6a-11)(6a-11)=(6a-11)^2=(6a)^2+\color{magenta}{2.(6a).(-11)}+(-11)^2=36a^2\color{magenta}{-132a}+121\)
8. \((x+6)(x+6)=(x+6)^2=x^2+\color{magenta}{2.x.6}+6^2=x^2\color{magenta}{+12x}+36\)
9. \((\color{red}{8p^3}\color{blue}{-13x})(\color{red}{-8p^3}\color{blue}{-13x})=\color{blue}{(-13x)}^2-\color{red}{(8p^3)}^2=169x^2-64p^{6}\)
10. \((\color{blue}{a}\color{red}{+12})(\color{blue}{a}\color{red}{-12})=\color{blue}{a}^2-\color{red}{12}^2=a^2-144\)
11. \((11b^3-12x)^2=(11b^3)^2\color{magenta}{+2.(11b^3).(-12x)}+(-12x)^2=121b^{6}\color{magenta}{-264b^3x}+144x^2\)
12. \((\color{red}{15b^5}\color{blue}{+12y})(\color{red}{-15b^5}\color{blue}{+12y})=\color{blue}{(12y)}^2-\color{red}{(15b^5)}^2=144y^2-225b^{10}\)