Simplify the following algebraic expressions: a) 6 − 5(2a + 2) b) 5(3x − 1) + 4(x + 2) c) −3(2y + 3) − (4y…

Question

Simplify the following algebraic expressions: a) 6 − 5(2a + 2) b) 5(3x − 1) + 4(x + 2) c) −3(2y + 3) − (4y − 2) d) x − 13 − (x − x2 + 12) e) x(x2 + 5x − 8) + x2 - 12 f) a(a2 + 5a − 2) − 2(a2 + 5a − 2)

ScanSolve AI Tutor · Accepted Answer

Here are the simplified expressions: a) Simplify 6 − 5(2a + 2) Step 1: Distribute the −5 into the parenthesis. 6 − 5(2a) − 5(2) 6 − 10a − 10 Step 2: Combine the constant terms. −10a + (6 − 10) −10a − 4 b) Simplify 5(3x − 1) + 4(x + 2) Step 1: Distribute 5 into the first parenthesis and 4 into the second. 5(3x) + 5(−1) + 4(x) + 4(2) 15x − 5 + 4x + 8 Step 2: Combine like terms. (15x + 4x) + (−5 + 8) 19x + 3 c) Simplify −3(2y + 3) − (4y − 2) Step 1: Distribute −3 into the first parenthesis and −1 into the second. −3(2y) − 3(3) − 1(4y) − 1(−2) −6y − 9 − 4y + 2 Step 2: Combine like terms. (−6y − 4y) + (−9 + 2) −10y − 7 d) Simplify x − 13 − (x − x² + 12) Step 1: Distribute −1 into the parenthesis. x − 13 − 1(x) − 1(−x²) − 1(12) x − 13 − x + x² − 12 Step 2: Combine like terms. x² + (x − x) + (−13 − 12) x² + 0 − 25 x² − 25 e) Simplify x(x² + 5x − 8) + x² − 12 Step 1: Distribute x into the parenthesis. x(x²) + x(5x) + x(−8) + x² − 12 x³ + 5x² − 8x + x² − 12 Step 2: Combine like terms. x³ + (5x² + x²) − 8x − 12 x³ + 6x² − 8x − 12 f) Simplify a(a² + 5a − 2) − 2(a² + 5a − 2) Step 1: Distribute a into the first parenthesis and −2 into the second. a(a²) + a(5a) + a(−2) − 2(a²) − 2(5a) − 2(−2) a³ + 5a² − 2a − 2a² − 10a + 4 Step 2: Combine like terms. a³ + (5a² − 2a²) + (−2a − 10a) + 4 a³ + 3a² − 12a + 4

Simplify the following algebraic expressions: a) 6 - 5(2a + 2) b) 5(3x - 1) + 4(x + 2) c) -3(2y + 3) - (4y - 2) d) x - 13 - (x - x2 + 12) e) x(x2 + 5x - 8) + x2 - 12 f) a(a2 + 5a - 2) - 2(a2 + 5a - 2)

Answers

Step-by-step solution

Part a· 2 steps

Distribute the $-5$ into the parenthesis.

Combine the constant terms.

Part b· 2 steps19x + 3

Distribute 5 into the first parenthesis and 4 into the second.

Combine like terms.

Part c· 2 steps-10y - 7

Distribute $-3$ into the first parenthesis and $-1$ into the second.

Combine like terms.

Part d· 2 steps
$x^2 - 25$

Distribute $-1$ into the parenthesis.

Combine like terms.

Part e· 2 steps
$x^3 + 6x^2 - 8x - 12$

Distribute $x$ into the parenthesis.

Combine like terms.

Part f· 2 steps
$a^3 + 3a^2 - 12a + 4$

Distribute $a$ into the first parenthesis and $-2$ into the second.

Combine like terms.

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More Mathematics Questions

Simplify the following algebraic expressions: a) 6 - 5(2a + 2) b) 5(3x - 1) + 4(x + 2) c) -3(2y + 3) - (4y - 2) d) x - 13 - (x - x2 + 12) e) x(x2 + 5x - 8) + x2 - 12 f) a(a2 + 5a - 2) - 2(a2 + 5a - 2)

Answers

Step-by-step solution

Part a· 2 steps

Distribute the −5-5−5 into the parenthesis.

Combine the constant terms.

Part b· 2 steps19x + 3

Distribute 5 into the first parenthesis and 4 into the second.

Combine like terms.

Part c· 2 steps-10y - 7

Distribute −3-3−3 into the first parenthesis and −1-1−1 into the second.

Combine like terms.

Part d· 2 stepsx2−25x^2 - 25x2−25

Distribute −1-1−1 into the parenthesis.

Combine like terms.

Part e· 2 stepsx3+6x2−8x−12x^3 + 6x^2 - 8x - 12x3+6x2−8x−12

Distribute xxx into the parenthesis.

Combine like terms.

Part f· 2 stepsa3+3a2−12a+4a^3 + 3a^2 - 12a + 4a3+3a2−12a+4

Distribute aaa into the first parenthesis and −2-2−2 into the second.

Combine like terms.

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More Mathematics Questions

Distribute the $-5$ into the parenthesis.

Distribute $-3$ into the first parenthesis and $-1$ into the second.

Part d· 2 steps
$x^2 - 25$

Distribute $-1$ into the parenthesis.

Part e· 2 steps
$x^3 + 6x^2 - 8x - 12$

Distribute $x$ into the parenthesis.

Part f· 2 steps
$a^3 + 3a^2 - 12a + 4$

Distribute $a$ into the first parenthesis and $-2$ into the second.