Question

How do you factor by grouping \[35xy-5x-56y+8\]?

Answer 1

Hint: In the given question, we need to factorize the given equation by grouping. Factorization means to write the given expression as a product of its factors. To solve the question, first we need to form the pair such that we will take common terms from each of the pairs given in the expression. Splitting the given expression into a multiplication of simpler expressions.

Complete step-by-step solution:
We have been given the expression as following:
\[35xy-5x-56y+8\]
Now, we form two group each having two terms and have a common term, we obtain
\[\left( 35xy-5x \right)+\left( -56y+8 \right)\]
Taking \[5x\] as a common from first two terms of the given expression i.e. \[\left( 35xy-5x \right)\] and \[-8\] as a common from last two terms we have i.e.\[\left( -56y+8 \right)\],
We obtain,
\[5x\left( 7y-1 \right)-8\left( 7y-1 \right)\]
Now on further simplification,
We take \[\left( 7y-1 \right)\] common and we have,
\[\left( 5x-8 \right)\left( 7y-1 \right)\]
Hence, the given expression is factored into factors.
Therefore, the factors of the given expression \[35xy-5x-56y+8\] are \[\left( 5x-8 \right)\left( 7y-1 \right)\].

Additional information: To solve the given expression, no formula has been used. We need to know only the basic factorization of linear equations.
To solve for the value of ‘x’ and ‘y’:
Taking common terms together and put them equal to 0, we get
\[\left( 5x-8 \right)\left( 7y-1 \right)\]= 0
Substituting each term equal to 0, we get
\[x=\dfrac{8}{5}\] and \[y=\dfrac{1}{7}\]
Therefore, \[x=\dfrac{8}{5}\] and \[y=\dfrac{1}{7}\] are the solution of the given expression.
(The above part has not been asked in the question but the knowledge of how to find the solution of the given expression is required in these types of questions.)

Note: Be careful while doing calculation because there is a possibility you might make some calculation mistakes and thus you will get the wrong answer. If you do not get the common term after forming a group try to rearrange the given expression in such a manner that you will get a common term and after that follow the same steps again for solving the question.