Question

factoriz the following?

Answer 1

$\bf HELLO \: \: DEAR,$

$\boxed{\bf 13}. \: \: \: \: \: \bf a^{2} + b^{2} + 2(ab + bc + ca)$

$\bf (a^{2} + b^{2} + 2ab) + 2(bc + ca)$

$\bf (a + b)^{2} + 2c(a + b)$

$\bf (a + b)(a + b + 2c)$

$\boxed{\bf 14}. \: \: \: \: \: \: \bf 4(x - y)^{2} - 12(x - y)(x + y) + 9(x + y)^{2}$

$\bf 4(x - y)(x - y) - 12(x - y)(x + y) + 9(x + y)(x + y) \\ \\ \bf 4(x - y)(x - y) - 6(x - y)(x + y) - 6(x - y)(x + y) + 9(x + y)(x + y) \\ \\ \bf 2(x - y)(2x - 2y - 3x - 3y) - 3(x + y)(2x - 2y - 3x - 3y) \\ \\ \bf 2(x - y)(-x - 5y) - 3(x + y)(-x - 5y) \\ \\ \bf (2x - 2y - 3x - 3y)(-x - 5y) \\ \\ \bf (-x - 5y)(-x - 5y) \\ \\ \bf(x + 5y)(x + 5y) \\ \\ \bf (x + 5y)^{2}$

$\boxed{\bf 15}. \: \: \bf a^{2} - b^{2} + 2bc - c^{2}$

$\bf a^{2} - (b^{2} - 2bc + c^{2}) \\ \\ \bf a^{2} - (b - c)^{2} \\ \\ \bf (a - b + c)(a + b - c)$

$\boxed{\bf 17}. \: \: \: \: \: \bf a^{2} + 4b^{2} - 4ab - 4c^{2}$

$\bf [a^{2} + (2b)^{2} - 2(a)(2b)] - 4c^{2}$

$\bf (a - 2b)^{2}) - (2c)^{2} \\ \\ \bf (a - 2b - 2c)(a - 2b + 2c)$

$\boxed{\bf 19}. \: \: \: \: \bf \: x^{4} + x^{2}y^{2} + y^{4}$

$\bf x^{4} + x^{2}y^{2} + y^{4} + (x^{2}y^{2} - x^{2}y^{2} ) \\ \\ \bf (x^{4} + 2x^{2}y^{2} + y^{4}) - x^{2}y^{2} \\ \\ \bf (x^{2} + y^{2})^{2} - (xy)^{2} \\ \\ \bf (x^{2} + y^{2} - xy)(x^{2} + y^{2} + xy)$

$\underline{\bf I \: \: HOPE \: \: ITS \: \: HELP \: \: YOU \: \: DEAR, THANKS}$

Answer 2

Hello friend

Sorry for late answering

Your answer is given in the attachment

I hope it will help you a lot

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