Simplify Algebraic Expressions using the Distributive Property 3

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Question 1 of 4

Simplify the expression

5 b (7 b - 3) - 12 b

$5b(7b-3)-12b$

Question 3 of 4

Simplify the expression

2 (6 y^{2} - 7 y - 9) - 10 y

$2(6y^2-7y-9)-10y$

	$5 b$ $5b$ $(7 b - 3) - 12 b$ $(7b-3)-12b$
$=$ $=$	$($ $($ $5 b$ $5b$ $\times 7 b) - ($ $xx7b)-($ $5 b$ $5b$ $\times 3) - 12 b$ $xx3)-12b$
$=$ $=$	$(35 \times b^{1 + 1}) - (15 \times b) - 12 b$ $(35xxb^(1+1))-(15xxb)-12b$	Multiplication property of exponents
$=$ $=$	$35 b^{2} - 15 b - 12 b$ $35b^2-15b-12b$

		$2$ $2$ $(6 y^{2} - 7 y - 9) - 10 y$ $(6y^2-7y-9)-10y$
	$=$ $=$	$($ $($ $2$ $2$ $\times 6 y^{2}) - ($ $xx6y^2)-($ $2$ $2$ $\times 7 y) - ($ $xx7y)-($ $2$ $2$ $\times 9) - 10 y$ $xx9)-10y$
	$=$ $=$	$12 y^{2} - 14 y - 18 - 10 y$ $12y^2-14y-18-10y$

		$4$ $4$ $(2 x^{2} + 3 x + 5) - 3 x$ $(2x^2+3x+5)-3x$
	$=$ $=$	$($ $($ $4$ $4$ $\times 2 x^{2}) + ($ $xx2x^2)+($ $4$ $4$ $\times 3 x) + ($ $xx3x)+($ $4$ $4$ $\times 5) - 3 x$ $xx5)-3x$
	$=$ $=$	$8 x^{2} + 12 x + 20 - 3 x$ $8x^2+12x+20-3x$

$8 x^{2} +$ $8x^2+$ $12 x$ $12x$ $+ 20 -$ $+20-$ $3 x$ $3x$	$=$ $=$	$8 x^{2} + ($ $8x^2+($ $12 x - 3 x$ $12x-3x$ $) + 20$ $)+20$
	$=$ $=$	$8 x^{2}$ $8x^2$ $+ 9 x$ $+9x$ $+ 20$ $+20$

$12 y^{2} -$ $12y^2-$ $14 y$ $14y$ $- 18 -$ $-18-$ $10 y$ $10y$	$=$ $=$	$12 y^{2}$ $12y^2$ $- 14 y - 10 y$ $-14y-10y$ $- 18$ $-18$
	$=$ $=$	$12 y^{2} - 24 y - 18$ $12y^2-24y-18$

$12 x^{2}$ $12x^2$ $+$ $+$ $3$ $3$ $-$ $-$ $2 x^{2}$ $2x^2$ $-$ $-$ $10$ $10$	$=$ $=$	$($ $($ $12 x^{2} - 2 x^{2}$ $12x^2-2x^2$ $) + ($ $)+($ $3 - 10$ $3-10$ $)$ $)$
	$=$ $=$	$10 x^{2}$ $10x^2$ $- 7$ $-7$