Question

factorize 5a^2-29ab-42b^2​

Answer 1

Answer:

answer in the attachment

Step-by-step explanation:

please mark as brainlist

Answer 2

$\large\underline{\sf{Solution-}}$

Given expression is

$\rm \: {5a}^{2} - 29ab - {42b}^{2}$

To factorize this expression, we use method of splitting of middle terms.

So, using splitting of middle terms, we get

$\rm \: {5a}^{2} - 35ab + 6ab - {42b}^{2}$

$\rm \: = \: 5a(a - 7b) + 6b(a - 7b)$

$\rm \: = \: (a - 7b)(5a + 6b)$

Hence,

$\rm\implies \: {5a}^{2} - 29ab - {42b}^{2} = \: (a - 7b)(5a + 6b)$

$\rule{190pt}{2pt}$

Basic Concept Used :-

Splitting of middle terms :-

In order to factorize  ax² + bx + c we have to find numbers m and n such that m + n = b and mn = ac.

After finding m and n, we split the middle term in the expression as nx + nx and get required factors by grouping the terms.

$\rule{190pt}{2pt}$

$\begin{gathered} \colorbox{powderblue}{ \boxed{ \begin{array}{c} \underline{\underline{ \color{orang} \text{Additional \: lnformation}}} \\ \\ & \color{re} \sf {(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2} \\ & \color{re} \sf {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2}\\ & \color{re} \sf {x}^{2} - {y}^{2} = (x + y)(x - y)\\ & \color{re} \sf {(x + y)}^{2} - {(x - y)}^{2} = 4xy\\ & \color{re} \sf {(x + y)}^{2} + {(x - y)}^{2} = 2( {x}^{2} + {y}^{2}) \\ \end{array}}}\end{gathered}$