Question

数学题分解因式

请写明步骤 每道10分 标好序号
1: 49(a-b)²-16(a+b)²
2: 16a4^+24a²b²+9b4^
3: 4-12(x-y)+9(x-y)²

Answer 1

1: 49(a-b)²-16(a+b)²=(7a-7b)²-(4a+4b)²=(7a-7b+4a+4b)(7a-7b-4a-4b)=(11a-3b)(3a-11b)
2: 16a4^+24a²b²+9b4^=(4a²)²+2×4a×3b+(3b²)²=(4a²+3b²)²
3: 4-12(x-y)+9(x-y)²=2²-2×2×3(x-y)+[3(x-y)²]=[2-3(x-y)]²=(2-3x+3y)²

Answer 2

1: 49(a-b)²-16(a+b)²=[7(a-b)+4(a+b)][7(a-b)-4(a+b)]
=(11a-3b)(3a-11b)
2: 16a4^+24a²b²+9b^4=(4a^2)^2+24a^2b^2+(3b^2)^2=(4a^2+3b^2)^2
3: 4-12(x-y)+9(x-y)²=2^2-2*2*3(x-y)+[3(x-y)]^2
=(2-3x+3y)^2

Answer 3

1: 49(a-b)²-16(a+b)²
=(7a-7b)²-(4a+4b)²
=(7a-7b+4a+4b)(7a-7b-4a-4b)
=(11a-3b)(3a-11b)

2:16a4^+24a²b²+9b^4
=(4a^2)^2+24a^2b^2+(3b^2)^2
=(4a^2+3b^2)^2

3:4-12(x-y)+9(x-y)²
=2²-2*2*(3x-3y)+(3x-3y)²
=(2-3x+3y)²

Answer 4

1: 49(a-b)²-16(a+b)²=[7(a-b)-4(a+b)]*[7(a-b)+4(a+b)]=(3a-11b)*(11a-3b)

2: 16a4^+24a²b²+9b4^=(4a²+3b²)²

3: 4-12(x-y)+9(x-y)²=[2-3(x-y)]²

Answer 5

1 =[7(a-b)+4(a+b)]*[7(a-b)-4(a+b)]
=(11a-3b)*(3a-11b)
2 =(4a2^+3b2^)*(4a2^+3b2^)
3 =[3(x-y)-2]*[3(x-y)-2]

Answer 6

1: 49(a-b)²-16(a+b)²=(49a²+49b²-98ab)-(16a²+16b²+32ab)
=49a²+49b²-98ab-16a²-16b²-32ab
=33a²+33b²-130ab
=(11a-3b)(3a-11b)
2: 16a4^+24a²b²+9b4^=(4a²)²+24a²b²+(3b²)²
=(4a²+3b²)²
3: 4-12(x-y)+9(x-y)²=[3(x-y)-2]²=(3x-3y-2)²