Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((p+3)(p+3)=(p+3)^2=p^2+\color{magenta}{2.p.3}+3^2=p^2\color{magenta}{+6p}+9\)
2. \((\color{blue}{b}\color{red}{-8})(\color{blue}{b}\color{red}{+8})=\color{blue}{b}^2-\color{red}{8}^2=b^2-64\)
3. \((8y^2+8s)^2=(8y^2)^2\color{magenta}{+2.(8y^2).(8s)}+(8s)^2=64y^{4}\color{magenta}{+128sy^2}+64s^2\)
4. \((\color{red}{-4a}\color{blue}{+8})(\color{red}{4a}\color{blue}{+8})=\color{blue}{8}^2-\color{red}{(4a)}^2=64-16a^2\)
5. \((\color{red}{-x^3}\color{blue}{+11})(\color{red}{x^3}\color{blue}{+11})=\color{blue}{11}^2-\color{red}{(x^3)}^2=121-x^{6}\)
6. \((8y+10)(8y+10)=(8y+10)^2=(8y)^2+\color{magenta}{2.(8y).10}+10^2=64y^2\color{magenta}{+160y}+100\)
7. \((\color{blue}{p}\color{red}{+4})(\color{blue}{p}\color{red}{-4})=\color{blue}{p}^2-\color{red}{4}^2=p^2-16\)
8. \((-12y^3+4q)(-12y^3+4q)=(-12y^3+4q)^2=(-12y^3)^2\color{magenta}{+2.(-12y^3).(4q)}+(4q)^2=144y^{6}\color{magenta}{-96qy^3}+16q^2\)
9. \((\color{red}{4a^2}\color{blue}{-10s})(\color{red}{-4a^2}\color{blue}{-10s})=\color{blue}{(-10s)}^2-\color{red}{(4a^2)}^2=100s^2-16a^{4}\)
10. \((y+8)(y+8)=(y+8)^2=y^2+\color{magenta}{2.y.8}+8^2=y^2\color{magenta}{+16y}+64\)
11. \((s-10)(s-10)=(s-10)^2=s^2+\color{magenta}{2.s.(-10)}+(-10)^2=s^2\color{magenta}{-20s}+100\)
12. \((a-9)(a-9)=(a-9)^2=a^2+\color{magenta}{2.a.(-9)}+(-9)^2=a^2\color{magenta}{-18a}+81\)