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Bài 3: 1) \( x^2 - 9 = 0 \) \( (x - 3)(x + 3) = 0 \) \( x - 3 = 0 \) hoặc \( x + 3 = 0 \) \( x = 3 \) hoặc \( x = -3 \) 2) \( 25 - x^2 = 0 \) \( (5 - x)(5 + x) = 0 \) \( 5 - x = 0 \) hoặc \( 5 + x = 0 \) \( x = 5 \) hoặc \( x = -5 \) 3) \( -x^2 + 36 = 0 \) \( x^2 = 36 \) \( x = 6 \) hoặc \( x = -6 \) 4) \( 4x^2 - 4 = 0 \) \( 4(x^2 - 1) = 0 \) \( x^2 - 1 = 0 \) \( (x - 1)(x + 1) = 0 \) \( x - 1 = 0 \) hoặc \( x + 1 = 0 \) \( x = 1 \) hoặc \( x = -1 \) 5) \( 4x^2 = 36 \) \( x^2 = 9 \) \( x = 3 \) hoặc \( x = -3 \) 6) \( 4x^2 - 36 = 0 \) \( 4(x^2 - 9) = 0 \) \( x^2 - 9 = 0 \) \( (x - 3)(x + 3) = 0 \) \( x - 3 = 0 \) hoặc \( x + 3 = 0 \) \( x = 3 \) hoặc \( x = -3 \) 7) \( (x + 3)^2 - (1 - x)^2 = 0 \) \( [(x + 3) - (1 - x)][(x + 3) + (1 - x)] = 0 \) \( (x + 3 - 1 + x)(x + 3 + 1 - x) = 0 \) \( (2x + 2)(4) = 0 \) \( 2x + 2 = 0 \) \( x = -1 \) 8) \( 49x^2 = (5x - 4)^2 \) \( (7x)^2 = (5x - 4)^2 \) \( 7x = 5x - 4 \) hoặc \( 7x = -(5x - 4) \) \( 7x - 5x = -4 \) hoặc \( 7x + 5x = 4 \) \( 2x = -4 \) hoặc \( 12x = 4 \) \( x = -2 \) hoặc \( x = \frac{1}{3} \) 9) \( 16(x - 1)^2 - 25 = 0 \) \( 16(x - 1)^2 = 25 \) \( (x - 1)^2 = \frac{25}{16} \) \( x - 1 = \frac{5}{4} \) hoặc \( x - 1 = -\frac{5}{4} \) \( x = \frac{9}{4} \) hoặc \( x = -\frac{1}{4} \) Đáp số: 1) \( x = 3 \) hoặc \( x = -3 \) 2) \( x = 5 \) hoặc \( x = -5 \) 3) \( x = 6 \) hoặc \( x = -6 \) 4) \( x = 1 \) hoặc \( x = -1 \) 5) \( x = 3 \) hoặc \( x = -3 \) 6) \( x = 3 \) hoặc \( x = -3 \) 7) \( x = -1 \) 8) \( x = -2 \) hoặc \( x = \frac{1}{3} \) 9) \( x = \frac{9}{4} \) hoặc \( x = -\frac{1}{4} \) Bài 4: 1) $(x+1)^2 = x^2 + 2 \cdot x \cdot 1 + 1^2 = x^2 + 2x + 1$ 2) $\left(\frac{1}{2} + x\right)^2 = \left(\frac{1}{2}\right)^2 + 2 \cdot \frac{1}{2} \cdot x + x^2 = \frac{1}{4} + x + x^2$ 3) $(6 - x)^2 = 6^2 - 2 \cdot 6 \cdot x + x^2 = 36 - 12x + x^2$ 4) $(5x + 1)^2 = (5x)^2 + 2 \cdot 5x \cdot 1 + 1^2 = 25x^2 + 10x + 1$ 5) $(2x - 3,5)^2 = (2x)^2 - 2 \cdot 2x \cdot 3,5 + (3,5)^2 = 4x^2 - 14x + 12,25$ 6) $(2x - 1)^2 = (2x)^2 - 2 \cdot 2x \cdot 1 + 1^2 = 4x^2 - 4x + 1$ 7) $(x + 2y^2)^2 = x^2 + 2 \cdot x \cdot 2y^2 + (2y^2)^2 = x^2 + 4xy^2 + 4y^4$ 8) $(2x + 3y^2)^2 = (2x)^2 + 2 \cdot 2x \cdot 3y^2 + (3y^2)^2 = 4x^2 + 12xy^2 + 9y^4$ 9) $(4x - 2y^2)^2 = (4x)^2 - 2 \cdot 4x \cdot 2y^2 + (2y^2)^2 = 16x^2 - 16xy^2 + 4y^4$