Question

factorize a) m²-13m-48 b) 64x²-169​

Answer 1

Step-by-step explanation:

(a)

$m^{2}-13m-48$ is a quadratic equation in the form of $ax^{2}+bx+c$, where

in this question, the variable $x$ is replaced with variable $m$.

So, $a=1,b=-13, c=-48$

Multiply $a$ and $c$ so that the sum of multiplier and multiplicand is equal to the value of $b$,

1 + (-48) ≠ -13 (1 × -48 = -48)

2 + (-24) ≠ -13 (2 × -24 = -48)

3 + (- 16) = -13 (3 × -16 = -48)

∴ $m^{2}-13m-48 = m^{2}+3m - 16m-48$

⇒ $m(m+3)-16(m+3)$

⇒ $(m-16)(m+3)$

∴ The factors of $m^{2}-13m-48$ are $(m-16)$  and $(m+3)$.

(b)

$64x^{2}-169$

$(8x)^{2}-(13)^{2}$

$(8x+13)(8x-13)$ $($∵ $a^{2}-b^{2}=(a+b)(a-b))$  

∴ The factors of $64x^{2}-169$ are $(8x+13)$ and $(8x-13)$.