Câu hỏi:
Giúp em bài tập về nhà Toán lớp 8 câu hỏi như sau: a)x^2-2xy+y^2-m^2+2mn-n^2 phan tich cac du thuc sau thanh nhan tu
b) a^2-10a+25-y^2-4yz-4z^2
c) x^2-2x-3
d) a^4+5a^3+15a-9
e) bc ( b+c)+ac (c-a)-ab (a+b)
g) 4x-4y+x^2-2xy+y^2
Trả lời 1:
Gia Sư Hoàng Khang gữi câu trả lời dành cho bạn:
a)$x^{2}$ – 2xy +$y^{2}$ – $m^{2}$ + 2mn – $n^{2}$
= ($x^{2}$ – 2xy +$y^{2}$) – ( $m^{2}$ – 2mn + $n^{2}$ )
= $(x-y)^{2}$ – $(m-n)^{2}$
= ( x – y + m – n ) ( x – y – m + n )
b) $a^{2}$ – 10a + 25 – $y^{2}$ -4yz – $4z^{2}$
= ( $a^{2}$ – 10a + 25 ) – ( $y^{2}$ + 4yz + $4z^{2}$ )
= ( $a^{2}$ – 10a + $5^{2}$ ) – [$y^{2}$ + 4yz + $(2z)^{2}$]
= $(a-5)^{2}$ – $(y+2z)^{2}$
= ( a – 5 + y + 2z ) ( a – 5 – y – 2z )
c) $x^{2}$ – 2x – 3
= $x^{2}$ + x – 3x – 3
= ( $x^{2}$ + x ) – ( 3x + 3 )
= x ( x + 1 ) – 3 ( x + 1 )
= ( x + 1 ) ( x – 3 )
d)$a^{4}$ + $5a^{3}$ + 15a – 9
= $a^{4}$ + $5a^{3}$ – $3a^{2}$ + $3a^{2}$ + 15a – 9
= ( $a^{4}$ + $5a^{3}$ – $3a^{2}$ ) + ( $3a^{2}$ + 15a – 9 )
= $a^{2}$ ( $a^{2}$ + 5a – 3 ) + 3 ( $a^{2}$ + 5a – 3 )
= ( $a^{2}$ + 5a – 3 ) ( $a^{2}$ + 3 )
e) bc ( b + c ) + ac ( c – a ) – ab ( a + b )
= = $b^{2}$c + $bc^{2}$ + $ac^{2}$ – $a^{2}$c – $a^{2}$b – $ab^{2}$
g) 4x – 4y + $x^{2}$ – 2xy + $y^{2}$
=( 4x – 4y ) + ( $x^{2}$ – 2xy + $y^{2}$ )
= 4 ( x – y ) + $(x-y)^{2}$
= ( x- y ) ( x – y + 4 )
