Question

factorise each of the following algebraic expression.
please help me
I will give 14 thanks plus follow​

Answer 1

Answer:

See this.

Step-by-step explanation:

$<marquee>Hope it helps you...Please mark this answer as the brainliest and follow me.</marquee>$

Answer 2

Question:

$1. \: 6 {x}^{2} - 5xy - 6 {y}^{2}$

$2. \: 1 - 2ab - ( {a}^{2} + {b}^{2} )$

$3. \: {(x + 2)}^{2} - 6(x + 2) + 9$

$4. \: {4x}^{4} + 1$

Answer:

$1. \: (2x - 3y)(3x + 2y)$

$2. \: \big[{a}^{2} + 6ab + {b}^{2}\big] - 1$

$3. {x}^{2} + {y}^{2} + 2x\big[2y - 3x\big] - 3$

$4. \: The \: answer \: is \: reconsisting.$

Step-by-step explanation:

$\bold{1. \: 6 {x}^{2} - 5xy - 6 {y}^{2} }$

Product :- -36 = -9 × 4

Sum :- -5 = -9 + 4

$\implies 6 {x}^{2} - 9xy + 4xy - 6 {y}^{2}$

$\implies 3x(2x - 3y) + 2y(2x - 3y)$

$\implies \boxed{(2x - 3y)(3x + 2y)}$

$\underline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }$

$\bold{2. \: 1 - 2ab - ( {a}^{2} + {b}^{2} )}$

$\implies 1 - 2ab - {(a + b)}^{2} - 2ab$

$\implies 1 - 4ab - {(a + b)}^{2}$

$\implies {(a + b)}^{2} + 4ab - 1$

$\implies {a}^{2} + 2ab + {b}^{2} + 4ab - 1$

$\implies \boxed{\big[{a}^{2} + 6ab + {b}^{2}\big] - 1}$

$\underline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }$

$\bold{3. \: {(x + 2)}^{2} - 6(x + 2) + 9}$

$\implies ( {x}^{2} + 4xy + {y}^{2} ) - 6x - 12 + 9$

$\implies {x}^{2} + 4xy + {y}^{2} - 6x - 3$

$\implies {x}^{2} + {y}^{2} + 4xy - 6x - 3$

$\implies \boxed{ {x}^{2} + {y}^{2} + 2x\big[2y - 3x\big] - 3}$

$\underline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }$

$\bf{4. \: {4x}^{4} + 1}$

$\implies {(2 {x}^{2} )}^{2} + {(1)}^{2}$

$\implies {(2 {x}^{2} + 1)}^{2} - 2(2 {x}^{2} )(1)$

$\implies {(2 {x}^{2} )}^{2} +2(2 {x}^{2} )(1) + {(1)}^{2} - 4 {x}^{2}$

$\implies {4x}^{4} + 4 {x}^{2} + 1 - 4 {x}^{2}$

$\implies \boxed{ {4x}^{4} + 1 }$

This answer is reconsisting.

$\underline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }$