Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

1. \((-12q^4-5b)^2\)
2. \((14p^4-15)(14p^4+15)\)
3. \((-9q-6)(-9q-6)\)
4. \((4a^4-15y)(4a^4+15y)\)
5. \((-14q^4+13)(-14q^4+13)\)
6. \((x-12)^2\)
7. \((10q-5)(-10q-5)\)
8. \((-7b-16)^2\)
9. \((12y^2+9q)(12y^2-9q)\)
10. \((12x^5+5b)^2\)
11. \((-2s^3-2y)^2\)
12. \((-6y^2+11)(-6y^2+11)\)

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((-12q^4-5b)^2=(-12q^4)^2\color{magenta}{+2.(-12q^4).(-5b)}+(-5b)^2=144q^{8}\color{magenta}{+120bq^4}+25b^2\)
2. \((\color{blue}{14p^4}\color{red}{-15})(\color{blue}{14p^4}\color{red}{+15})=\color{blue}{(14p^4)}^2-\color{red}{(-15)}^2=196p^{8}-225\)
3. \((-9q-6)(-9q-6)=(-9q-6)^2=(-9q)^2+\color{magenta}{2.(-9q).(-6)}+(-6)^2=81q^2\color{magenta}{+108q}+36\)
4. \((\color{blue}{4a^4}\color{red}{-15y})(\color{blue}{4a^4}\color{red}{+15y})=\color{blue}{(4a^4)}^2-\color{red}{(-15y)}^2=16a^{8}-225y^2\)
5. \((-14q^4+13)(-14q^4+13)=(-14q^4+13)^2=(-14q^4)^2\color{magenta}{+2.(-14q^4).13}+13^2=196q^{8}\color{magenta}{-364q^4}+169\)
6. \((x-12)^2=x^2+\color{magenta}{2.x.(-12)}+(-12)^2=x^2\color{magenta}{-24x}+144\)
7. \((\color{red}{10q}\color{blue}{-5})(\color{red}{-10q}\color{blue}{-5})=\color{blue}{(-5)}^2-\color{red}{(10q)}^2=25-100q^2\)
8. \((-7b-16)^2=(-7b)^2+\color{magenta}{2.(-7b).(-16)}+(-16)^2=49b^2\color{magenta}{+224b}+256\)
9. \((\color{blue}{12y^2}\color{red}{+9q})(\color{blue}{12y^2}\color{red}{-9q})=\color{blue}{(12y^2)}^2-\color{red}{(9q)}^2=144y^{4}-81q^2\)
10. \((12x^5+5b)^2=(12x^5)^2\color{magenta}{+2.(12x^5).(5b)}+(5b)^2=144x^{10}\color{magenta}{+120bx^5}+25b^2\)
11. \((-2s^3-2y)^2=(-2s^3)^2\color{magenta}{+2.(-2s^3).(-2y)}+(-2y)^2=4s^{6}\color{magenta}{+8s^3y}+4y^2\)
12. \((-6y^2+11)(-6y^2+11)=(-6y^2+11)^2=(-6y^2)^2\color{magenta}{+2.(-6y^2).11}+11^2=36y^{4}\color{magenta}{-132y^2}+121\)