Use the methods you discovered in 2.2 and 3.2 and simplify the following: 4.1.1 (x-3)(x+5)= 4.1.2 (x-9)2=

Mathematics
Use the methods you discovered in 2.2 and 3.2 and simplify the following: 4.1.1 (x-3)(x+5)= 4.1.2 (x-9)2=

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Answer

\text{*x^2 + 2x - 15*}

Here are the solutions for the given algebraic expressions:

4.1 Use the methods you discovered in 2.2 and 3.2 and simplify the following:

4.1.1 (x−3)(x+5)(x-3)(x+5) Step 1: Multiply the first terms of each binomial. x×x=x2x \times x = x^2 Step 2: Multiply the outer terms. x×5=5xx \times 5 = 5x Step 3: Multiply the inner terms. −3×x=−3x-3 \times x = -3x Step 4: Multiply the last terms of each binomial. −3×5=−15-3 \times 5 = -15 Step 5: Combine all terms and simplify by adding like terms. x2+5x−3x−15=x2+2x−15x^2 + 5x - 3x - 15 = x^2 + 2x - 15 ∗x2+2x−15∗\boxed{*x^2 + 2x - 15*}

4.1.2 (x−9)2(x-9)^2 Step 1: Square the first term. x2x^2 Step 2: Multiply 22 by the product of the two terms in the bracket. 2×x×(−9)=−18x2 \times x \times (-9) = -18x Step 3: Square the last term. (−9)2=81(-9)^2 = 81 Step 4: Write the answer by combining the terms. x2−18x+81x^2 - 18x + 81 ∗x2−18x+81∗\boxed{*x^2 - 18x + 81*}

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4.1 Use the methods you discovered in 2.2 and 3.2 and simplify the following: 4.1.1 (x-3)(x+5) Step 1: Multiply the first terms of each binomial.

Use the methods you discovered in 2.2 and 3.2 and simplify the following: 4.1.1 (x-3)(x+5)= 4.1.2 (x-9)2=
Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI Answer
Here are the solutions for the given algebraic expressions: 4.1 Use the methods you discovered in 2.2 and 3.2 and simplify the following: 4.1.1 (x-3)(x+5) Step 1: Multiply the first terms of each binomial. x × x = x^2 Step 2: Multiply the outer terms. x × 5 = 5x Step 3: Multiply the inner terms. -3 × x = -3x Step 4: Multiply the last terms of each binomial. -3 × 5 = -15 Step 5: Combine all terms and simplify by adding like terms. x^2 + 5x - 3x - 15 = x^2 + 2x - 15 x^2 + 2x - 15 4.1.2 (x-9)^2 Step 1: Square the first term. x^2 Step 2: Multiply 2 by the product of the two terms in the bracket. 2 × x × (-9) = -18x Step 3: Square the last term. (-9)^2 = 81 Step 4: Write the answer by combining the terms. x^2 - 18x + 81 x^2 - 18x + 81 3 done, 2 left today. You're making progress.