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\(=\left[4x-4y\right]^2-\left(5x+5y\right)^2\)
\(=\left(4x-4y+5x-5y\right)\left(4x-4y-5x+5y\right)\)
\(=\left(9x-9y\right)\left(y-x\right)\)
\(=-9\left(x-y\right)^2\)
16(x-y)2-25(x+y)2
=16(x-y)2-25(x-y)2
=(16-25)(x-y)2
=-9(x-y)2
(4(x-y))2 - (5(x+y))2 = (4(x-y) +5(x+y))(4(x-y) -5(x+y))
(4x-4y +5x+5y)(4x-4y-5x-5y)
= -(9x +y)(x+9y)
6, \(x^2-1+2xy+y^2=\left(x+y\right)^2-1=\left(x+y-1\right)\left(x+y+1\right)\)
7, \(4x^2-12x+9-y^2=\left(2x-3\right)^2-y^2=\left(2x-3-y\right)\left(2x-3+y\right)\)
8, \(16x^2-4y^2+4y-1=16x^2-\left(2y-1\right)^2=\left(4x-2y+1\right)\left(4x+2y-1\right)\)
9, \(25-x^2-12x-36=25-\left(x+6\right)^2=\left(5-x-6\right)\left(5+x+5\right)=-\left(x+1\right)\left(x+10\right)\)
10, \(x^2-9-5\left(x+3\right)=\left(x-3\right)\left(x+3\right)-5\left(x+3\right)=\left(x+3\right)\left(x-8\right)\)
7, 4x mũ 2 - 12x + 9 - y mũ 2 = -(y-2x+3) (y+2x-3)
8, 16x mũ 2 - 4y mũ 2 + 4y - 1 = -(2y - 4x - 1) (2y+4x-1)
9, 25 - x mũ 2 - 12x - 36 = -(x+1) (x+11)
10, x mũ 2 - 9 - 5 ( x + 3 ) = (x-8) (x+3)
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Câu hỏi của Phạm Đỗ Bảo Ngọc - Toán lớp 8 - Học trực tuyến OLM
\(=5^{^2}.\left(x+5\right)^2-3^2.\left(x+7\right)^2\)
\(=\left(5x+25\right)^2-\left(3x+21\right)^2\)
\(=\left(5x+25+3x+21\right)\left(5x+25-3x-21\right)\)
\(=\left(8x+46\right)\left(2x+4\right)\)
\(=4\left(2x+23\right)\left(x+2\right)\)
= 52 ( x + 5)2 - 32 (x +7)2
=[ 5 ( x +5) ]2 - [ 3 ( x + 7) ]2
= ( 5x + 25)2 - ( 3x + 21)2
= ( 5x + 25 - 3x - 21) - ( 5x + 25 + 3x + 21)
= ( 2x +4) - ( 8x +46)
= -6x - 42
= -6 ( x + 7)
25(x-y)2-16(x+y)2
=[5(x-y)]2-[4(x+y)]2
=[5x-5y]2-[4x+4y]2
=(5x-5y+4x+4y)[(5x-5y)-(4x+4y)]
=(9x-y)(x-9y)
\(9\left(x+5\right)^2-\left(x-7\right)^2\)
\(=\left(3x+15\right)^2-\left(x-7\right)^2\)
\(=\left(3x+15-x+7\right)\left(3x+15+x-7\right)\)
\(=\left(2x+22\right)\left(4x+8\right)\)
\(=2\left(x+11\right).4\left(x+2\right)\)
\(=8\left(x+11\right)\left(x+2\right)\)