# Ontbinden in factoren (2)

#### Zonder de gemeenschappelijke factor af. Ontbind verder in factoren indien mogelijk.

1. $$-27x^{7}+3x^{5}$$
2. $$-12p^{7}+75p^{5}$$
3. $$-64b^{10}+112b^{7}p-49b^{4}p^2$$
4. $$-36q^{10}+49q^{2}$$
5. $$-2p^{4}+32p^{2}$$
6. $$-49p^{12}-70p^{7}-25p^{2}$$
7. $$-2p^{7}-28p^{6}-98p^{5}$$
8. $$384p^{8}+288p^{6}+54p^{4}$$
9. $$216s^{7}+504s^{5}y+294s^{3}y^2$$
10. $$-3a^{5}-48a^{4}-192a^{3}$$
11. $$-147a^{12}-252a^{7}y-108a^{2}y^2$$
12. $$-18p^{18}+50p^{2}$$

#### Zonder de gemeenschappelijke factor af. Ontbind verder in factoren indien mogelijk.

##### Verbetersleutel

1. $$-27x^{7}+3x^{5}=-3x^{5}(9x^{2}-1)=-3x^{5}(3x+1)(3x-1)$$
2. $$-12p^{7}+75p^{5}=-3p^{5}(4p^{2}-25)=-3p^{5}(2p+5)(2p-5)$$
3. $$-64b^{10}+112b^{7}p-49b^{4}p^2=-b^{4}(64b^{6}-112b^3p+49p^2)=-b^{4}(8b^3-7p)^2$$
4. $$-36q^{10}+49q^{2}=-q^{2}(36q^{8}-49)=-q^{2}(6q^4+7)(6q^4-7)$$
5. $$-2p^{4}+32p^{2}=-2p^{2}(p^2-16)=-2p^{2}(p-4)(p+4)$$
6. $$-49p^{12}-70p^{7}-25p^{2}=-p^{2}(49p^{10}+70p^5+25)=-p^{2}(7p^5+5)^2$$
7. $$-2p^{7}-28p^{6}-98p^{5}=-2p^{5}(p^2+14p+49)=-2p^{5}(p+7)^2$$
8. $$384p^{8}+288p^{6}+54p^{4}=6p^{4}(64p^{4}+48p^2+9)=6p^{4}(8p^2+3)^2$$
9. $$216s^{7}+504s^{5}y+294s^{3}y^2=6s^{3}(36s^{4}+84s^2y+49y^2)=6s^{3}(6s^2+7y)^2$$
10. $$-3a^{5}-48a^{4}-192a^{3}=-3a^{3}(a^2+16a+64)=-3a^{3}(a+8)^2$$
11. $$-147a^{12}-252a^{7}y-108a^{2}y^2=-3a^{2}(49a^{10}+84a^5y+36y^2)=-3a^{2}(7a^5+6y)^2$$
12. $$-18p^{18}+50p^{2}=-2p^{2}(9p^{16}-25)=-2p^{2}(3p^8+5)(3p^8-5)$$
Oefeningengenerator vanhoeckes.be/wiskunde 2022-06-27 07:14:35