Expand the following expressions: (4a − 1)(2a + 3) and (2x + 5)(3x − 4).

Question

ScanSolve AI Tutor · Accepted Answer

Here are the solutions to the problems.

Multiply the first terms of $(4a - 1)(2a + 3)$ .
$(4a)(2a) = 8a^2$
Multiply the outer terms.
$(4a)(3) = 12a$
Multiply the inner terms.
$(-1)(2a) = -2a$
Multiply the last terms.
$(-1)(3) = -3$
Combine all terms and simplify.
$8a^2 + 12a - 2a - 3 = 8a^2 + 10a - 3$
The expanded form is:
$\boxed{8a^2 + 10a - 3}$
Multiply the first terms of $(2x + 5)(3x - 4)$ .
$(2x)(3x) = 6x^2$
Multiply the outer terms.
$(2x)(-4) = -8x$
Multiply the inner terms.
$(5)(3x) = 15x$
Multiply the last terms.
$(5)(-4) = -20$
Combine all terms and simplify.
$6x^2 - 8x + 15x - 20 = 6x^2 + 7x - 20$
The expanded form is:
$\boxed{6x^2 + 7x - 20}$

Expand the following expressions: (4a - 1)(2a + 3) and (2x + 5)(3x - 4).