Question

Factorise by grouping =4m (3n-5)+(3n-5)​

Answer 1

$\large\textsf\red{QUESTION:}$

Factorise by grouping =4m (3n-5)+(3n-5)

$\large\textsf\green{ANSWER:}$

$\textsf\green{(3n - 5) (4m + 1)}$

$\textsf\blue{\underline{SOLUTION:}}$

$\textsf{Step\:1:}$ Remove parentheses

$\implies\textsf{4m (3n - 5) + 3n - 5}$

$\textsf{Step\:2:}$ Simplify each term

Apply the distributive property

$\implies\textsf{4m (3n) + 4m × -5 + 3n - 5}$

Rewrite using commutive property of multiplication

$\implies\textsf{4 × 3mn + 4m × -5 + 3n - 5}$

Multiply -5 by 4

$\implies\textsf{4 × 3mn - 20m + 3n - 5}$

Multiply 4 by 3

$\implies\textsf{12mn - 20m + 3n - 5}$

$\textsf{Step\:3:}$ Factor out the greatest common factor from each group

Group the first two terms and the last two terms

$\implies\textsf{(12mn - 20m) + 3n - 5}$

Factor out the greatest common factor (GCF) from each group

$\implies\textsf{4m (3n - 5) + 1 (3n - 5)}$

$\textsf{Lastly:}$ Factor the polynomial by factoring out the greatest common factor, 3n - 5

$\green\implies\textsf\green{(3n - 5) (4m + 1)}$

hope this help! :)