F.3 to F.4 Maths暑期作業 Factorization?

(A) Factorization
Fctorization the following expressions.
1. (4m－n)(2m+n)+(7n－m)(2m+n)
=[(4m－n)+(7n－m)](2m+n)
=(3m－6n)(2m+n)
=3(m－2n)(2m+n)
2a. (2a+b)(x+y)－b(y－2)
=2ax+2ay+bx+by－by+2b
=2ax+2ay+bx+2b
b. (5x+3y)(2x－y)-(y－x)(y－2x)
=10x^2－5xy+6xy－3y^2-(y^2－3xy+2x^2)
=10x^2－5xy+6xy－3y^2－y^2+3xy－2x^2
=8x^2－4xy－4y^2
=4(2x^2－xy－y^2)
=4(2x+y)(x－y)
3a. a^2bc－a+ab^2c－b－abc^2+c
=(a^2bc+ab^2c－abc^2)+(－a－b+c)
=abc(a+b－c)－(a+b－c)
=(abc－1)(a+b－c)
b. 2ax－4ay－4bx+8by+6cx－12cy
=(2ax－4ay)+(－4bx+8by)+(6cx－12cy)
=2a(x－2y)－4b(x－2y)+6c(x－2y)
=(2a－4b+6c)(x－2y)
=2(a－2b+3c)(x－2y)
4. It is given that 2x^2－5x+1=－1 and xy^2=3.Eva claims that the value of 8x^3 y^2－20x^2 y^2+4xy^2 is 12.Do you agree? Explain your answer.
Sol
8x^3y^2－20x^2y^2+4xy^2
=8x^2*(xy^2)－20x*(xy^2)+4(xy^2)
=8x^2*3－20x*3+4*3
=24x^2－60x+12
=12*2x^2－60x+12
=12*(5x－2)－60x+12
=60x－24-60x+12
=－12