25a^2-b^2 e 81j^2-k^2 x x^2-81y^2 25p^2-36q^2 h 4d^2-25e^2 Fully factorise: f s^2t^2-9 16x^2-49y^2 8x^2-2 49x^2-y^2z^2 p 12-27x^2 2y^2-8x^2 d 9a-16a^3

Let's factorize each expression step by step:<br /><br />1. \(25a^2 - b^2\)<br /> - This is a difference of squares: \( (5a)^2 - b^2 \)<br /> - Factor as: \((5a - b)(5a + b)\)<br /><br />2. \(81j^2 - k^2\)<br /> - This is a difference of squares: \((9j)^2 - k^2\)<br /> - Factor as: \((9j - k)(9j + k)\)<br /><br />3. \(x^2 - 81y^2\)<br /> - This is a difference of squares: \(x^2 - (9y)^2\)<br /> - Factor as: \((x - 9y)(x + 9y)\)<br /><br />4. \(25p^2 - 36q^2\)<br /> - This is a difference of squares: \((5p)^2 - (6q)^2\)<br /> - Factor as: \((5p - 6q)(5p + 6q)\)<br /><br />5. \(4d^2 - 25e^2\)<br /> - This is a difference of squares: \((2d)^2 - (5e)^2\)<br /> - Factor as: \((2d - 5e)(2d + 5e)\)<br /><br />6. \(s^2t^2 - 9\)<br /> - This is a difference of squares: \((st)^2 - 3^2\)<br /> - Factor as: \((st - 3)(st + 3)\)<br /><br />7. \(16x^2 - 49y^2\)<br /> - This is a difference of squares: \((4x)^2 - (7y)^2\)<br /> - Factor as: \((4x - 7y)(4x + 7y)\)<br /><br />8. \(8x^2 - 2\)<br /> - Factor out the common factor: \(2(4x^2 - 1)\)<br /> - Recognize that \(4x^2 - 1\) is a difference of squares: \((2x)^2 - 1^2\)<br /> - Factor as: \(2(2x - 1)(2x + 1)\)<br /><br />9. \(49x^2 - y^2z^2\)<br /> - This is a difference of squares: \((7x)^2 - (yz)^2\)<br /> - Factor as: \((7x - yz)(7x + yz)\)<br /><br />10. \(12 - 27x^2\)<br /> - Factor out the common factor: \(3(4 - 9x^2)\)<br /> - Recognize that \(4 - 9x^2\) is a difference of squares: \(2^2 - (3x)^2\)<br /> - Factor as: \(3(2 - 3x)(2 + 3x)\)<br /><br />11. \(2y^2 - 8x^2\)<br /> - Factor out the common factor: \(2(y^2 - 4x^2)\)<br /> - Recognize that \(y^2 - 4x^2\) is a difference of squares: \(y^2 - (2x)^2\)<br /> - Factor as: \(2(y - 2x)(y + 2x)\)<br /><br />12. \(9a - 16a^3\)<br /> - Factor out the common factor: \(a(9 - 16a^2)\)<br /> - Recognize that \(9 - 16a^2\) is a difference of squares: \(3^2 - (4a)^2\)<br /> - Factor as: \(a(3 - 4a)(3 + 4a)\)<br /><br />So, the fully factorized forms are:<br /><br />1. \((5a - b)(5a + b)\)<br />2. \((9j - k)(9j + k)\)<br />3. \((x - 9y)(x + 9y)\)<br />4. \((5p - 6q)(5p + 6q)\)<br />5. \((2d - 5e)(2d + 5e)\)<br />6. \((st - 3)(st + 3)\)<br />7. \((4x - 7y)(4x + 7y)\)<br />8. \(2(2x - 1)(2x + 1)\)<br />9. \((7x - yz)(7x + yz)\)<br />10. \(3(2 - 3x)(2 + 3x)\)<br />11. \(2(y - 2x)(y + 2x)\)<br />12. \(a(3 - 4a)(3 + 4a)\)