Question

1) 6ab+21b+8a+28 2) 8x²+12xy+10xz+15yz 3) 30x³y-15x²y²-20x⁴y²+10x³y³ 4) -24a⁴b⁴+8a³b⁴+12a²b³-4ab³

Answer 1

Ответ:

1)6ab+21b+8a+28=(6ab+21b)+(8a+28)=3b(2a+7)+4(2a+7)=(2a+7)(3b+4)

2)8x²+12xy+10xz+15yz=(8x²+10xz)+(12xy+15yz)=2x(4x+5z)+3y(4x+5z)=(4x+5z)(2x+3y)

3)30x³y-15x²y²-20x⁴y²+10x³y³=(30x³y-15x²y²)+(20x⁴y²-10x³y³)= =15x²y(2x-y)+10x³y²(2x-y)=(2x-y)(15x²y+10x³y²)

4)-24a⁴b⁴+8a³b⁴+12a²b³-4ab³=(-24a⁴b⁴+12a²b³)+(8a³b⁴-4ab³)=+12a²b³(-2a²b+1)-4ab³(2a²b+1)=2a²b+1)(12a²b³-4ab³)

Объяснение:

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Answer 2

It appears that you have provided four algebraic expressions, and you might want to simplify or factor them. Here are the simplified forms of these expressions:

1. 6ab + 21b + 8a + 28:

This expression can be factored by grouping: 6ab + 21b + 8a + 28 = (6ab + 21b) + (8a + 28) = 3b(2a + 7) + 4(2a + 7) = (3b + 4)(2a + 7)

So, the simplified expression is (3b + 4)(2a + 7).

2. 8x² + 12xy + 10xz + 15yz:

This expression cannot be simplified further. It remains as 8x² + 12xy + 10xz + 15yz.

3. 30x³y - 15x²y² - 20x⁴y² + 10x³y³:

This expression can be simplified by factoring out common terms: 30x³y - 15x²y² - 20x⁴y² + 10x³y³ = 5x³y(6 - 3xy - 4x²y + 2x²y²)

So, the simplified expression is 5x³y(6 - 3xy - 4x²y + 2x²y²).

4. -24a⁴b⁴ + 8a³b⁴ + 12a²b³ - 4ab³:

This expression can be simplified by factoring out common terms: -24a⁴b⁴ + 8a³b⁴ + 12a²b³ - 4ab³ = -4ab³(6a³b³ - 2a²b² - 3ab + 1)

So, the simplified expression is -4ab³(6a³b³ - 2a²b² - 3ab + 1).