Question

(4a²+6ab+9b²) × (2a+3b)​

Answer 1

Answer:

$8a^3 + 27b^3 + 36a^2b + 54ab^2$

Step-by-step explanation:

(4a²+12ab+9b²) × (2a+3b)​

When we look at (4a²+12ab+9b²), we can identify that it is in the $A^2 + 2AB + B^2$ form.

$A^2 + 2AB + B^2$ = $(A+B)^{2}$

Applying this identity,

(4a²+12ab+9b²) = $(2a+3b)^{2}$

$(2a+3b)^{2}$ × $(2a+3b)$

= $(2a+3b)^{3}$

$(A+B)^{3} = A^3 + B^3 + 3AB(A+B)$

$(2a+3b)^{3} = (2a)^{3} + (3b)^3 + [3(2a)(3b)(2a+3b)]$

= $8a^3 + 27b^3 + 36a^2b + 54ab^2$