Question

因式分解，谢谢！

(1).
5a^2+26ab+5b^2+11ac+7bc+2c^2
(2)
7x^2+56xy-5x-40y
那么(5a+b)(a+5b)+2c(5a+b)+c(a+5b)+2c²到(5a+b+c)(a+5b+2c)呢？

Answer 1

(1)

5a²+26ab+5b²+11ac+7bc+2c²
=(5a+b)(a+5b)+11ac+7bc+2c²
=(5a+b)(a+5b)+10ac+2bc+ac+5bc+2c²
=(5a+b)(a+5b)+2c(5a+b)+c(a+5b)+2c²
=(5a+b+c)(a+5b+2c)

(2)

7x²+56xy-5x-40y
=7x(x+8y)-5(x+8y)
=(7x-5)(x+8y)

Answer 2

5a^2+26ab+5b^2+11ac+7bc+2c^2
=5a^2+ab+ac+25ab+5b^2+5bc+10ac+2bc+2c^2
=a(5a+b+c)+5b(5a+b+c)+2c(5a+b+c)
=(a+5b+2c)(5a+b+c)

7x^2+56xy-5x-40y
=7x(x+8y)-5(x+8y)
=(7x-5)(x+8y)