Question

Factorise 16c^3 + 54d^3​

Answer 1

Step-by-step explanation:

$\huge\bold\red{QUESTION}$

Factorise 16c^3 + 54d^3

$\huge\bold\blue{ANSWER}$

16c³+54d³

=2(8c³+27d³)

=2[ (2c)³+(3d)³]

=2[ (2c+3d)(4c²+9d²-6cd)]

(As a³+b³=(a+b)(a²-ab+b²))

=2(2c+3d)(4c²+9d²-6cd)

$\huge\blue\textbf{ADDITIONAL INFORMATION}$

• a²+b²+2ab=(a+b)²
• a²+b²-2ab=(a-b)²
• a²-b²=(a+b)(a-b)
• a³+b³=(a+b)(a²-ab+b²)
• a³-b³=(a-b)(a²+ab+b²)
• a³+b³+c³-3abc=(a+b+c)(a²+b²+c²-ab-bc-ca)

SUM PRODUCT FACTORISATION METHOD

If the polynomial is of the form ax²+ b x + c

then we split the b into 'm' and 'n' in such a way that

mn=ac

m+n=b

so we write it as

ax²+mx+nx+c

=ax²+mx+nx+mn/a

After factorisation

we write

(ax+m)(nx+c)

Answer 2

Answer: Please refer to the attachment