Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((-14q-8)(-14q-8)=(-14q-8)^2=(-14q)^2+\color{magenta}{2.(-14q).(-8)}+(-8)^2=196q^2\color{magenta}{+224q}+64\)
2. \((-11y^2+8)^2=(-11y^2)^2\color{magenta}{+2.(-11y^2).8}+8^2=121y^{4}\color{magenta}{-176y^2}+64\)
3. \((10y-4)^2=(10y)^2+\color{magenta}{2.(10y).(-4)}+(-4)^2=100y^2\color{magenta}{-80y}+16\)
4. \((\color{blue}{y}\color{red}{+2})(\color{blue}{y}\color{red}{-2})=\color{blue}{y}^2-\color{red}{2}^2=y^2-4\)
5. \((\color{blue}{4a^4}\color{red}{+2y})(\color{blue}{4a^4}\color{red}{-2y})=\color{blue}{(4a^4)}^2-\color{red}{(2y)}^2=16a^{8}-4y^2\)
6. \((\color{blue}{q}\color{red}{-5})(\color{blue}{q}\color{red}{+5})=\color{blue}{q}^2-\color{red}{5}^2=q^2-25\)
7. \((11q+4)^2=(11q)^2+\color{magenta}{2.(11q).4}+4^2=121q^2\color{magenta}{+88q}+16\)
8. \((6s^3-7)^2=(6s^3)^2\color{magenta}{+2.(6s^3).(-7)}+(-7)^2=36s^{6}\color{magenta}{-84s^3}+49\)
9. \((\color{blue}{11x^5}\color{red}{-8q})(\color{blue}{11x^5}\color{red}{+8q})=\color{blue}{(11x^5)}^2-\color{red}{(-8q)}^2=121x^{10}-64q^2\)
10. \((-12y^5-12a)(-12y^5-12a)=(-12y^5-12a)^2=(-12y^5)^2\color{magenta}{+2.(-12y^5).(-12a)}+(-12a)^2=144y^{10}\color{magenta}{+288ay^5}+144a^2\)
11. \((y+11)^2=y^2+\color{magenta}{2.y.11}+11^2=y^2\color{magenta}{+22y}+121\)
12. \((q-7)(q-7)=(q-7)^2=q^2+\color{magenta}{2.q.(-7)}+(-7)^2=q^2\color{magenta}{-14q}+49\)