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Chapter 5: Problem 15

Remove the brackets from the following and simplify the result: (a) \((a+3)(a-5)\) (b) \((2 b+6)(b-7)\) (c) \((3 c+4)(2 c-1)\) (d) \((5 d+8)(-2 d-1)\)

Short Answer

Expert verified
Question: Simplify the following expressions and write the final expressions: a) (a+3)(a-5) b) (2b+6)(b-7) c) (3c+4)(2c-1) d) (5d+8)(-2d-1) Answer: a) a^2 - 2a - 15 b) 2b^2 - 8b - 42 c) 6c^2 + 5c - 4 d) -10d^2 - 21d - 8

Step by step solution

01

Simplifying expression (a)

Distribute the terms, according to the distributive property: \((a+3)(a-5) = a(a-5) + 3(a-5)\) Apply the distributive property: \(a(a) - a(5) + 3(a) - 3(5)\) Combine like terms and simplify: \(a^2 - 5a + 3a - 15\) Final expression: \(a^2 - 2a - 15\)
02

Simplifying expression (b)

Distribute the terms, according to the distributive property: \((2b+6)(b-7) = 2b(b-7) + 6(b-7)\) Apply the distributive property: \(2b(b) - 2b(7) + 6(b) - 6(7)\) Combine like terms and simplify: \(2b^2 - 14b + 6b - 42\) Final expression: \(2b^2 - 8b - 42\)
03

Simplifying expression (c)

Distribute the terms, according to the distributive property: \((3c+4)(2c-1) = 3c(2c-1) + 4(2c-1)\) Apply the distributive property: \(3c(2c) - 3c(1) + 4(2c) - 4(1)\) Combine like terms and simplify: \(6c^2 - 3c + 8c - 4\) Final expression: \(6c^2 + 5c - 4\)
04

Simplifying expression (d)

Distribute the terms, according to the distributive property: \((5d+8)(-2d-1) = 5d(-2d-1) + 8(-2d-1)\) Apply the distributive property: \(5d(-2d) - 5d(1) - 8(2d) - 8(1)\) Combine like terms and simplify: \(-10d^2 - 5d - 16d - 8\) Final expression: \(-10d^2 - 21d - 8\)

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Most popular questions from this chapter

Simplify \(\frac{2 x-5}{10}-\frac{3 x-2}{15}\)

Simplify \(\frac{x+2}{x^{2}+3 x+2} .\)

Factorise (a) \(x^{2}+x\), (b) \(3 x^{2}+6 x\) (c) \(9 x^{2}-12 x\).

Express \(\frac{1}{s}+\frac{1}{s^{2}}\) as a single fraction.

In each case, simplify the given expression, if possible. \(a b+b a\)
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