Question

factorize:
1]49x^4-154x^2y^2+9y^4
2]25a^4-34a^2x^2+9x^4
3]1225x^4+31x^2y^2+64y^4

Answer 1

$1) \red{ 49x^4-154x^2y^2+9y^4} \\= (7x^{2})^{2} - 2 \times (7x^{2}) \times (3y^{2}) + (3y^{2})^{2} - 112x^{2}y^{2} \\= ( 7x^{2} - 3y^{2})^{2} - (4\sqrt{7}xy)^{2} \\= [(7x^{2} - 3y^{2}) + 4\sqrt{7}xy ] [(7x^{2} - 3y^{2}) - 4\sqrt{7}xy]\\\green {= (7x^{2} - 3y^{2}+ 4\sqrt{7}xy)(7x^{2} - 3y^{2}- 4\sqrt{7}xy)}$

$2. \red{ 25a^4-34a^2x^2+9x^4} \\= (5a^{2})^{2} - 2 \times (5a^{2}) \times (3x^{2}) + ( 3x^{2})^{2} - 4 a^{2} x^{2} \\= ( 5a^{2} - 3x^{2})^{2} - (2ax)^{2} \\= [ ( 5a^{2} - 3x^{2}) + 2ax] [ ( 5a^{2} - 3x^{2}) - 2ax]\\\green {= ( 5a^{2} - 3x^{2} + 2ax)( 5a^{2} - 3x^{2} - 2ax)}$

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