Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((2y^4+12)^2=(2y^4)^2\color{magenta}{+2.(2y^4).12}+12^2=4y^{8}\color{magenta}{+48y^4}+144\)
2. \((\color{blue}{q}\color{red}{+12})(\color{blue}{q}\color{red}{-12})=\color{blue}{q}^2-\color{red}{12}^2=q^2-144\)
3. \((5p+7)(5p+7)=(5p+7)^2=(5p)^2+\color{magenta}{2.(5p).7}+7^2=25p^2\color{magenta}{+70p}+49\)
4. \((-14a^2+9)(-14a^2+9)=(-14a^2+9)^2=(-14a^2)^2\color{magenta}{+2.(-14a^2).9}+9^2=196a^{4}\color{magenta}{-252a^2}+81\)
5. \((\color{blue}{10b^3}\color{red}{+13s})(\color{blue}{10b^3}\color{red}{-13s})=\color{blue}{(10b^3)}^2-\color{red}{(13s)}^2=100b^{6}-169s^2\)
6. \((x-15)(x-15)=(x-15)^2=x^2+\color{magenta}{2.x.(-15)}+(-15)^2=x^2\color{magenta}{-30x}+225\)
7. \((\color{red}{x^3}\color{blue}{+6})(\color{red}{-x^3}\color{blue}{+6})=\color{blue}{6}^2-\color{red}{(x^3)}^2=36-x^{6}\)
8. \((8p^2+12x)^2=(8p^2)^2\color{magenta}{+2.(8p^2).(12x)}+(12x)^2=64p^{4}\color{magenta}{+192p^2x}+144x^2\)
9. \((4a+7)(4a+7)=(4a+7)^2=(4a)^2+\color{magenta}{2.(4a).7}+7^2=16a^2\color{magenta}{+56a}+49\)
10. \((\color{blue}{16y^2}\color{red}{+14p})(\color{blue}{16y^2}\color{red}{-14p})=\color{blue}{(16y^2)}^2-\color{red}{(14p)}^2=256y^{4}-196p^2\)
11. \((-7q-9)^2=(-7q)^2+\color{magenta}{2.(-7q).(-9)}+(-9)^2=49q^2\color{magenta}{+126q}+81\)
12. \((-7x^3+4)(-7x^3+4)=(-7x^3+4)^2=(-7x^3)^2\color{magenta}{+2.(-7x^3).4}+4^2=49x^{6}\color{magenta}{-56x^3}+16\)