Question

(-2x²+3)²= (-3a²-4b)² (-10m³+0,1m)²= (-5y³+0,2y)²=

Answer 1

Ответ:

1. $4x^4-12x^2+9$
2. $9a^4+24a^2b+16b^2$
3. $0,01m^2-2m^4+100mn^6$
4. $0,04y^2-2y^4+25y^6$

Объяснение:

1. $(-2x^2+3)^2 = (3-2x^2)^2 = 9-12x^2+4x^4 = 4x^4-12x^2+9$
2. $(-3a^2-4b)^2 = (-3a^2)^2-2*(-3)a^2*4b+(4b)^2 = 9a^4+24a^2b+16b^2$
3. $(-10^3+0,1m)^2 = (-10m^3+\frac{1}{10}m)^2 = (\frac{1}{10}m-10m^3)^2 = 0,01m^2-2m^4+100mn^6$
4. $(-5y^3+0,2y)^2 = (-5y^3+\frac{1}{5}y)^2 = (\frac{1}{5}y-5y^3)^2 = 0,04y^2-2y^4+25y^6$

Answer 2

Let's simplify the given expressions step by step:

1. (-2x²+3)²

To square a binomial, we can use the formula (a - b)² = a² - 2ab + b². In this case, a = -2x² and b = 3.

(-2x² + 3)² = (-2x²)² - 2(-2x²)(3) + 3² = 4x⁴ + 12x² - 36x² + 9 = 4x⁴ - 24x² + 9

Therefore, (-2x²+3)² simplifies to 4x⁴ - 24x² + 9.

2. (-3a²-4b)²

Using the same formula, a = -3a² and b = -4b.

(-3a² - 4b)² = (-3a²)² - 2(-3a²)(-4b) + (-4b)² = 9a⁴ + 24a²b + 16b²

So, (-3a²-4b)² simplifies to 9a⁴ + 24a²b + 16b².

3. (-10m³+0.1m)²

Similarly, a = -10m³ and b = 0.1m.

(-10m³ + 0.1m)² = (-10m³)² - 2(-10m³)(0.1m) + (0.1m)² = 100m⁶ - 2m⁴ + 0.01m²

Thus, (-10m³+0.1m)² simplifies to 100m⁶ - 2m⁴ + 0.01m².

4. (-5y³+0.2y)²

Applying the formula, a = -5y³ and b = 0.2y.

(-5y³ + 0.2y)² = (-5y³)² - 2(-5y³)(0.2y) + (0.2y)² = 25y⁶ + 2y⁴ + 0.04y²

Hence, (-5y³+0.2y)² simplifies to 25y⁶ + 2y⁴ + 0.04y².

To summarize:

• (-2x²+3)² simplifies to 4x⁴ - 24x² + 9.
• (-3a²-4b)² simplifies to 9a⁴ + 24a²b + 16b².
• (-10m³+0.1m)² simplifies to 100m⁶ - 2m⁴ + 0.01m².
• (-5y³+0.2y)² simplifies to 25y⁶ + 2y⁴ + 0.04y².