Question

1. use the box method to distribute and simplify ((6x^{2}+2x + 5)(x - 5)).
2. use the box method to distribute and simplify ((-2x - 4)(-4x^{2}+x - 6)).
3. use the box method to distribute and simplify ((-4x^{2}-6x + 5)(4x + 2)).

Explanation:

Problem 17: $(6x^2 + 2x + 5)(x - 5)$

Step1: Create 3x2 box, fill terms

Top row: $6x^2, 2x, 5$; Left column: $x, -5$

	$6x^2$	$2x$	$5$
$-5$	$-30x^2$	$-10x$	$-25$

Step2: Combine all box terms

$6x^3 + 2x^2 + 5x - 30x^2 - 10x - 25$

Step3: Combine like terms

$6x^3 + (2x^2-30x^2) + (5x-10x) -25$
$=6x^3 -28x^2 -5x -25$

Step1: Create 2x3 box, fill terms

Top row: $-4x^2, x, -6$; Left column: $-2x, -4$

	$-4x^2$	$x$	$-6$
$-4$	$16x^2$	$-4x$	$24$

Step2: Combine all box terms

$8x^3 -2x^2 +12x +16x^2 -4x +24$

Step3: Combine like terms

$8x^3 + (-2x^2+16x^2) + (12x-4x) +24$
$=8x^3 +14x^2 +8x +24$

Step1: Create 3x2 box, fill terms

Top row: $-4x^2, -6x, 5$; Left column: $4x, 2$

	$-4x^2$	$-6x$	$5$
$2$	$-8x^2$	$-12x$	$10$

Step2: Combine all box terms

$-16x^3 -24x^2 +20x -8x^2 -12x +10$

Step3: Combine like terms

$-16x^3 + (-24x^2-8x^2) + (20x-12x) +10$
$=-16x^3 -32x^2 +8x +10$

Answer:

$6x^3 - 28x^2 - 5x - 25$

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Problem 18: $(-2x - 4)(-4x^2 + x - 6)$