Given two algebraic expressions E1 = 2x2 - 4x + 6 and E2 = 8x2 + 4x − 2, find their sum, difference, value at…

Question

Given two algebraic expressions E1 = 2x2 - 4x + 6 and E2 = 8x2 + 4x − 2, find their sum, difference, value at x=1, and value of sum at x=−2.

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Here are the solutions for each part of the problem. Let the two algebraic expressions be: E₁ = 2x² − 4x + 6; E₂ = 8x² + 4x − 2 a) Find the sum of the two expressions. Step 1: Add the two expressions. E₁ + E₂ = (2x² − 4x + 6) + (8x² + 4x − 2) Step 2: Combine like terms. E₁ + E₂ = (2x² + 8x²) + (−4x + 4x) + (6 − 2); E₁ + E₂ = 10x² + 0x + 4; E₁ + E₂ = 10x² + 4 b) Find the difference between the two expressions. Step 1: Subtract the second expression from the first. E₁ − E₂ = (2x² − 4x + 6) − (8x² + 4x − 2) Step 2: Distribute the negative sign. E₁ − E₂ = 2x² − 4x + 6 − 8x² − 4x + 2 Step 3: Combine like terms. E₁ − E₂ = (2x² − 8x²) + (−4x − 4x) + (6 + 2); E₁ − E₂ = −6x² − 8x + 8; E₁ − E₂ = −6x² − 8x + 8; c) If x = 1, find the number value of each expression. Step 1: Substitute x=1 into E₁. E₁ = 2(1)² − 4(1) + 6; E₁ = 2(1) − 4 + 6; E₁ = 2 − 4 + 6; E₁ = −2 + 6; E₁ = 4; Step 2: Substitute x=1 into E₂. E₂ = 8(1)² + 4(1) − 2; E₂ = 8(1) + 4 − 2; E₂ = 8 + 4 − 2; E₂ = 12 − 2; E₂ = 10; d) If x = −2, what is the number value of the sum of the expressions? Step 1: Use the sum expression from part a), S(x) = 10x² + 4. Step 2: Substitute x=−2 into the sum expression. S(−2) = 10(−2)² + 4; S(−2) = 10(4) + 4; S(−2) = 40 + 4; S(−2) = 44; e) If x = −3, what is the number value of the difference of the expressions? Step 1: Use the difference expression from part b), D(x) = −6x² − 8x + 8. Step 2: Substitute x=−3 into the difference expression. D(−3) = −6(−3)² − 8(−3) + 8; D(−3) = −6(9) − (−24) + 8; D(−3) = −54 + 24 + 8; D(−3) = −30 + 8; D(−3) = −22

Given two algebraic expressions E1 = 2x2 − 4x + 6 and E2 = 8x2 + 4x − 2, find their sum, difference, value at x=1, and value of sum at x=-2.

Answers

Step-by-step solution

Part a· 2 steps

Add the two expressions.

Combine like terms.

Part b· 3 steps
$-6x^2 - 8x + 8$

Subtract the second expression from the first.

Distribute the negative sign.

Combine like terms.

Part c· 2 steps4

Substitute $x=1$ into $E_1$ .

Substitute $x=1$ into $E_2$ .

Part d· 2 steps44

Use the sum expression from part a), $S(x) = 10x^2 + 4$ .

Substitute $x=-2$ into the sum expression.

Part e· 2 steps-22

Use the difference expression from part b), $D(x) = -6x^2 - 8x + 8$ .

Substitute $x=-3$ into the difference expression.

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More Mathematics Questions

Given two algebraic expressions E1 = 2x2 − 4x + 6 and E2 = 8x2 + 4x − 2, find their sum, difference, value at x=1, and value of sum at x=-2.

Answers

Step-by-step solution

Part a· 2 steps

Add the two expressions.

Combine like terms.

Part b· 3 steps−6x2−8x+8-6x^2 - 8x + 8−6x2−8x+8

Subtract the second expression from the first.

Distribute the negative sign.

Combine like terms.

Part c· 2 steps4

Substitute x=1x=1x=1 into E1E_1E1​.

Substitute x=1x=1x=1 into E2E_2E2​.

Part d· 2 steps44

Use the sum expression from part a), S(x)=10x2+4S(x) = 10x^2 + 4S(x)=10x2+4.

Substitute x=−2x=-2x=−2 into the sum expression.

Part e· 2 steps-22

Use the difference expression from part b), D(x)=−6x2−8x+8D(x) = -6x^2 - 8x + 8D(x)=−6x2−8x+8.

Substitute x=−3x=-3x=−3 into the difference expression.

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Part b· 3 steps
$-6x^2 - 8x + 8$

Substitute $x=1$ into $E_1$ .

Substitute $x=1$ into $E_2$ .

Use the sum expression from part a), $S(x) = 10x^2 + 4$ .

Substitute $x=-2$ into the sum expression.

Use the difference expression from part b), $D(x) = -6x^2 - 8x + 8$ .

Substitute $x=-3$ into the difference expression.