Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((p-2)(p-2)=(p-2)^2=p^2+\color{magenta}{2.p.(-2)}+(-2)^2=p^2\color{magenta}{-4p}+4\)
2. \((-4x^2+5a)(-4x^2+5a)=(-4x^2+5a)^2=(-4x^2)^2\color{magenta}{+2.(-4x^2).(5a)}+(5a)^2=16x^{4}\color{magenta}{-40ax^2}+25a^2\)
3. \((\color{red}{12x^2}\color{blue}{-16p})(\color{red}{-12x^2}\color{blue}{-16p})=\color{blue}{(-16p)}^2-\color{red}{(12x^2)}^2=256p^2-144x^{4}\)
4. \((9b^2+9)(9b^2+9)=(9b^2+9)^2=(9b^2)^2\color{magenta}{+2.(9b^2).9}+9^2=81b^{4}\color{magenta}{+162b^2}+81\)
5. \((9x^3+11b)(9x^3+11b)=(9x^3+11b)^2=(9x^3)^2\color{magenta}{+2.(9x^3).(11b)}+(11b)^2=81x^{6}\color{magenta}{+198bx^3}+121b^2\)
6. \((5p^4-5)^2=(5p^4)^2\color{magenta}{+2.(5p^4).(-5)}+(-5)^2=25p^{8}\color{magenta}{-50p^4}+25\)
7. \((b-9)^2=b^2+\color{magenta}{2.b.(-9)}+(-9)^2=b^2\color{magenta}{-18b}+81\)
8. \((\color{red}{2p^2}\color{blue}{-7y})(\color{red}{-2p^2}\color{blue}{-7y})=\color{blue}{(-7y)}^2-\color{red}{(2p^2)}^2=49y^2-4p^{4}\)
9. \((-8q^3+13x)^2=(-8q^3)^2\color{magenta}{+2.(-8q^3).(13x)}+(13x)^2=64q^{6}\color{magenta}{-208q^3x}+169x^2\)
10. \((\color{blue}{16y}\color{red}{+16})(\color{blue}{16y}\color{red}{-16})=\color{blue}{(16y)}^2-\color{red}{(16)}^2=256y^2-256\)
11. \((5a^2-14)^2=(5a^2)^2\color{magenta}{+2.(5a^2).(-14)}+(-14)^2=25a^{4}\color{magenta}{-140a^2}+196\)
12. \((3x^4-10)(3x^4-10)=(3x^4-10)^2=(3x^4)^2\color{magenta}{+2.(3x^4).(-10)}+(-10)^2=9x^{8}\color{magenta}{-60x^4}+100\)