Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((-7b^5-8a)^2=(-7b^5)^2\color{magenta}{+2.(-7b^5).(-8a)}+(-8a)^2=49b^{10}\color{magenta}{+112ab^5}+64a^2\)
2. \((-5p+9)(-5p+9)=(-5p+9)^2=(-5p)^2+\color{magenta}{2.(-5p).9}+9^2=25p^2\color{magenta}{-90p}+81\)
3. \((y+4)(y+4)=(y+4)^2=y^2+\color{magenta}{2.y.4}+4^2=y^2\color{magenta}{+8y}+16\)
4. \((p-15)^2=p^2+\color{magenta}{2.p.(-15)}+(-15)^2=p^2\color{magenta}{-30p}+225\)
5. \((\color{blue}{-8x}\color{red}{-4})(\color{blue}{-8x}\color{red}{+4})=\color{blue}{(-8x)}^2-\color{red}{(-4)}^2=64x^2-16\)
6. \((-9y^3-13s)(-9y^3-13s)=(-9y^3-13s)^2=(-9y^3)^2\color{magenta}{+2.(-9y^3).(-13s)}+(-13s)^2=81y^{6}\color{magenta}{+234sy^3}+169s^2\)
7. \((\color{red}{7a^2}\color{blue}{+6})(\color{red}{-7a^2}\color{blue}{+6})=\color{blue}{6}^2-\color{red}{(7a^2)}^2=36-49a^{4}\)
8. \((-12q+13)(-12q+13)=(-12q+13)^2=(-12q)^2+\color{magenta}{2.(-12q).13}+13^2=144q^2\color{magenta}{-312q}+169\)
9. \((-4q^4-x)^2=(-4q^4)^2\color{magenta}{+2.(-4q^4).(-x)}+(-x)^2=16q^{8}\color{magenta}{+8q^4x}+1x^2\)
10. \((-5p^4+5a)(-5p^4+5a)=(-5p^4+5a)^2=(-5p^4)^2\color{magenta}{+2.(-5p^4).(5a)}+(5a)^2=25p^{8}\color{magenta}{-50ap^4}+25a^2\)
11. \((\color{blue}{x}\color{red}{+5})(\color{blue}{x}\color{red}{-5})=\color{blue}{x}^2-\color{red}{5}^2=x^2-25\)
12. \((\color{blue}{p}\color{red}{-2})(\color{blue}{p}\color{red}{+2})=\color{blue}{p}^2-\color{red}{2}^2=p^2-4\)