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=

Question

ScanSolve AI Tutor · Accepted 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 $(x-3)(x+5)$

Multiply the first terms of each binomial.
$x \times x = x^2$
Multiply the outer terms.
$x \times 5 = 5x$
Multiply the inner terms.
$-3 \times x = -3x$
Multiply the last terms of each binomial.
$-3 \times 5 = -15$
Combine all terms and simplify by adding like terms.
$x^2 + 5x - 3x - 15 = x^2 + 2x - 15$ \boxed{\text{x^2 + 2x - 15}}
4.1.2 $(x-9)^2$
Square the first term.
$x^2$
Multiply 2 by the product of the two terms in the bracket.
$2 \times x \times (-9) = -18x$
Square the last term.
$(-9)^2 = 81$
Write the answer by combining the terms.
$x^2 - 18x + 81$ \boxed{\text{x^2 - 18x + 81}}

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=