Solve for the following algebraic expressions by substitution and expansion of brackets.

Question

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Here are the solutions to the problems. Question 1: Substitution 1.1 Step 1: Substitute x=3 into the expression 2(x+4)². 2(3+4)² Step 2: Perform the operation inside the parenthesis. 2(7)² Step 3: Calculate the square. 2(49) Step 4: Multiply. 98 The value is: 98 1.2 Step 1: Substitute x=8 and y=9 into the expression √[3]x+7√(y). √[3]8+7√(9) Step 2: Simplify the terms under the radicals. √[3]15√(9) Step 3: Calculate the cube root and the square root. √[3]153 The value is: √[3]153 1.3 Step 1: Substitute x=2 and y=3 into the expression 6x⁴y² − 18x³y³ + 12x²y. 6(2)⁴(3)² − 18(2)³(3)³ + 12(2)²(3) Step 2: Calculate the powers. 6(16)(9) − 18(8)(27) + 12(4)(3) Step 3: Perform the multiplications in each term. 864 − 3888 + 144 Step 4: Perform the additions and subtractions. −3024 + 144 −2880 The value is: −2880 Question 2: Expanding Brackets 2.1 Step 1: Expand the product (x+4)(x−3) using the FOIL method (First, Outer, Inner, Last). x · x + x · (−3) + 4 · x + 4 · (−3) x² − 3x + 4x − 12 Step 2: Combine like terms. x² + x − 12 The expanded expression is: x²+x−12 2.2 Step 1: Distribute x² to each term inside the parenthesis (2x−4). x²(2x) − x²(4) 2x³ − 4x² The expanded expression is: 2x³−4x² Question 3: Factorize the following expressions 3.1 Step 1: Find the greatest common factor (GCF) of x² and 4x. The GCF is x. Step 2: Factor out the GCF. x(x+4) The factored expression is: x(x+4) 3.2 Step 1: Find the GCF of 25xy² and 15x²y. The GCF of 25 and 15 is 5. The GCF of x and x² is x. The GCF of y² and y is y. So, the overall GCF is 5xy. Step 2: Factor out the GCF. 5xy(5y + 3x) The factored expression is: 5xy(5y+3x) 3.3 Step 1: Find the GCF of 8x³y² and 12x²y³. The GCF of 8 and 12 is 4. The GCF of x³ and x² is x². The GCF of y² and y³ is y². So, the overall GCF is 4x²y². Step 2: Factor out the GCF. 4x²y²(2x − 3y) The factored expression is: 4x²y²(2x−3y) 3.4 Step 1: Factor the quadratic expression x²−x−12. We need two numbers that multiply to −12 and add to −1. These numbers are 3 and −4. (x+3)(x−4) The factored expression is: (x+3)(x−4) 3.5 Step 1: Find the GCF of 6x⁴y², −18x³y³, and 12x²y. The GCF of 6, 18, and 12 is 6. The GCF of x⁴, x³, and x² is x². The GCF of y², y³, and y is y. So, the overall GCF is 6x²y. Step 2: Factor out the GCF. 6x²y(x²y − 3xy² + 2) The factored expression is: 6x²y(x²y−3xy²+2) 3.6 Step 1: Factor the quadratic expression x²−9x+20. We need two numbers that multiply to 20 and add to −9. These numbers are −4 and −5. (x−4)(x−5) The factored expression is: (x−4)(x−5) 3.7 Step 1: Subtract x²−4x−5 from 2x²+x−1. (2x²+x−1) − (x²−4x−5) Step 2: Distribute the negative sign. 2x²+x−1 − x²+4x+5 Step 3: Combine like terms. (2x²−x²) + (x+4x) + (−1+5) x² + 5x + 4 Step 4: Factor the resulting quadratic expression x²+5x+4. We need two numbers that multiply to 4 and add to 5. These numbers are 1 and 4. (x+1)(x+4) The factored expression is: (x+1)(x+4)

Solve for the following algebraic expressions by substitution and expansion of brackets.

Step-by-step solution

Part 1

Part 1.1· 4 steps

Substitute x=3x=3x=3 into the expression 2(x+4)22(x+4)^22(x+4)2.

Perform the operation inside the parenthesis.

Calculate the square.

Multiply.

Part 1.2· 3 steps

Substitute x=8x=8x=8 and y=9y=9y=9 into the expression x+73y\frac{\sqrt[3]{x+7}}{\sqrt{y}}y​3x+7​​.

Simplify the terms under the radicals.

Calculate the cube root and the square root.

Part 1.3· 4 steps

Substitute x=2x=2x=2 and y=3y=3y=3 into the expression 6x4y2−18x3y3+12x2y6x^4y^2 - 18x^3y^3 + 12x^2y6x4y2−18x3y3+12x2y.

Calculate the powers.

Perform the multiplications in each term.

Perform the additions and subtractions.

Part 2

Part 2.1· 2 steps

Expand the product (x+4)(x−3)(x+4)(x-3)(x+4)(x−3) using the FOIL method (First, Outer, Inner, Last).

Combine like terms.

Part 2.2· 1 step

Distribute x2x^2x2 to each term inside the parenthesis (2x−4)(2x-4)(2x−4).

Part 3

Part 3.1· 2 steps

Find the greatest common factor (GCF) of x2x^2x2 and 4x4x4x.

Factor out the GCF.

Part 3.2· 2 steps

Find the GCF of 25xy225xy^225xy2 and 15x2y15x^2y15x2y.

Factor out the GCF.

Part 3.3· 2 steps

Find the GCF of 8x3y28x^3y^28x3y2 and 12x2y312x^2y^312x2y3.

Factor out the GCF.

Part 3.4· 1 step

Factor the quadratic expression x2−x−12x^2-x-12x2−x−12.

Part 3.5· 2 steps

Find the GCF of 6x4y26x^4y^26x4y2, −18x3y3-18x^3y^3−18x3y3, and 12x2y12x^2y12x2y.

Factor out the GCF.

Part 3.6· 1 step

Factor the quadratic expression x2−9x+20x^2-9x+20x2−9x+20.

Part 3.7· 4 steps

Subtract x2−4x−5x^2-4x-5x2−4x−5 from 2x2+x−12x^2+x-12x2+x−1.

Distribute the negative sign.

Combine like terms.

Factor the resulting quadratic expression x2+5x+4x^2+5x+4x2+5x+4.

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More Mathematics Questions

Substitute $x=3$ into the expression $2(x+4)^2$ .

Substitute $x=8$ and $y=9$ into the expression $\frac{\sqrt[3]{x+7}}{\sqrt{y}}$ .

Substitute $x=2$ and $y=3$ into the expression $6x^4y^2 - 18x^3y^3 + 12x^2y$ .

Expand the product $(x+4)(x-3)$ using the FOIL method (First, Outer, Inner, Last).

Distribute $x^2$ to each term inside the parenthesis $(2x-4)$ .

Find the greatest common factor (GCF) of $x^2$ and $4x$ .

Find the GCF of $25xy^2$ and $15x^2y$ .

Find the GCF of $8x^3y^2$ and $12x^2y^3$ .

Factor the quadratic expression $x^2-x-12$ .

Find the GCF of $6x^4y^2$ , $-18x^3y^3$ , and $12x^2y$ .

Factor the quadratic expression $x^2-9x+20$ .

Subtract $x^2-4x-5$ from $2x^2+x-1$ .

Factor the resulting quadratic expression $x^2+5x+4$ .