Expansion of algebraic Expressions

Question

ScanSolve AI Tutor · Accepted Answer

Here are the step-by-step expansions for each algebraic expression:

1) $(x+4)(x+5)$

Distribute the terms.
$x(x+5) + 4(x+5)$
Multiply each term inside the parentheses.
$x^2 + 5x + 4x + 20$
Combine like terms.
$x^2 + 9x + 20$
The expansion is $\boxed{x^2 + 9x + 20}$ .

2) $(x-3)(x+7)$
Distribute the terms.
$x(x+7) - 3(x+7)$
Multiply each term inside the parentheses.
$x^2 + 7x - 3x - 21$
Combine like terms.
$x^2 + 4x - 21$
The expansion is $\boxed{x^2 + 4x - 21}$ .

3) $(2x+1)(x-6)$
Distribute the terms.
$2x(x-6) + 1(x-6)$
Multiply each term inside the parentheses.
$2x^2 - 12x + x - 6$
Combine like terms.
$2x^2 - 11x - 6$
The expansion is $\boxed{2x^2 - 11x - 6}$ .

4) $(3x-2)(x+4)$
Distribute the terms.
$3x(x+4) - 2(x+4)$
Multiply each term inside the parentheses.
$3x^2 + 12x - 2x - 8$
Combine like terms.
$3x^2 + 10x - 8$
The expansion is $\boxed{3x^2 + 10x - 8}$ .

5) $(x+6)(2x-3)$
Distribute the terms.
$x(2x-3) + 6(2x-3)$
Multiply each term inside the parentheses.
$2x^2 - 3x + 12x - 18$
Combine like terms.
$2x^2 + 9x - 18$
The expansion is $\boxed{2x^2 + 9x - 18}$ .

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Step-by-step solution